https://wiki.math.wisc.edu/api.php?action=feedcontributions&user=Jcobb2&feedformat=atomUW-Math Wiki - User contributions [en]2024-03-29T15:09:40ZUser contributionsMediaWiki 1.39.5https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25698Graduate Algebraic Geometry Seminar Fall 20232023-12-11T18:36:14Z<p>Jcobb2: /* Being an audience member */</p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' Van Vleck B119<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/fNgXzpn7QAJM4Ybo9 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="200" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="200" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
| bgcolor="#BCD2EE" width="400" align="center" |'''Abstract'''<br />
|-<br />
| bgcolor="#E0E0E0" |September 13<br />
| bgcolor="#C6D46E" | Peter Wei<br />
| bgcolor="#BCE2FE" | Introduction to the Cartier Isomorphism (Pretalk)<br />
| bgcolor="#BCE2FE" | This is a preparatory talk for Josh Mundinger's talk on Friday. We discuss the Cartier isomorphism. <br />
|-<br />
| bgcolor="#E0E0E0" |September 20<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |September 27<br />
| bgcolor="#C6D46E" |Yifan Wei<br />
| bgcolor="#BCE2FE" |p-torsions in the p-adic land and de Rham cohomology<br />
| bgcolor="#BCE2FE" | Following Tate, we will try to visualize an elliptic curve over Cp, specifically, the p-adic disk near identity. Logarithm in the p-adic land provides a nice linearization to the problem, and we'll explore what this all means. If time permits, I'll sketch the proof of Hodge-Tate decomposition. (You know something like this is coming.)<br />
|-<br />
| bgcolor="#E0E0E0" |October 4<br />
| bgcolor="#C6D46E" |Owen Goff<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 11<br />
| bgcolor="#C6D46E" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 18<br />
| bgcolor="#C6D46E" |Alex Hof<br />
| bgcolor="#BCE2FE" |Why Does Normalization Resolve Singularities in Codimension 1?<br />
| bgcolor="#BCE2FE" |We review the definition of the normalization of an algebraic variety, discuss the geometric intuition for it, and explain why normalizing removes codimension-1 singularities. This talk is intended to be accessible to people taking first-semester algebraic geometry.<br />
|-<br />
| bgcolor="#E0E0E0" | October 25<br />
| bgcolor="#C6D46E" |Jack Messina<br />
| bgcolor="#BCE2FE" |Variations of Hodge Structure and Hodge Modules<br />
| bgcolor="#BCE2FE" | This talk aims to introduce Hodge modules. We will start with the classical variation of Hodge structure, and then cover some background on perverse sheaves and D-modules. From here, we can introduce pure Hodge modules. We end by mentioning mixed Hodge modules and the Saito vanishing theorem.<br />
|-<br />
| bgcolor="#E0E0E0" | November 1<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | November 8<br />
| bgcolor="#C6D46E" |John Cobb<br />
| bgcolor="#BCE2FE" |Likelihood Geometry<br />
| bgcolor="#BCE2FE" |Maximum likelihood estimation (MLE) is a fundamental task in statistics. June Huh and Bernd Sturmfels wrote a long paper that explores how characteristics of the MLE problem for algebraic statistical models are reflected in the geometry of the likelihood correspondence, a variety that ties together observed data and their maximum likelihood estimators. I’ll define these objects, frame some questions (with partial answers) about them, and give some cool facts coming from algebraic statistics. This will be adapted from a much shorter talk, so there will be plenty of time for tangents and questions!<br />
|-<br />
| bgcolor="#E0E0E0" | November 15<br />
| bgcolor="#C6D46E" |Peter Wei<br />
| bgcolor="#BCE2FE" |Pretalk for Purnaprajna Bangere's talk<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 22<br />
| bgcolor="#C6D46E" |Thanksgiving Break<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 29<br />
| bgcolor="#C6D46E" |Yanbo Chen<br />
| bgcolor="#BCE2FE" |An Introduction to Homotopy Theory<br />
| bgcolor="#BCE2FE" |The Brown Representability theorem tells us that each generilized cohomology theory is representable, then use the suspension theorem, we get a sequence of spaces and some relations between them. This is a simple model for spectrum in algebraic topology. In this talk we will discuss this notion, give some geometric examples and explore one important problem: how to get a ``good<nowiki>''</nowiki> category for spectra.<br />
|-<br />
| bgcolor="#E0E0E0" | December 9<br />
| bgcolor="#C6D46E" | Kevin Dao<br />
| bgcolor="#BCE2FE" |Introduction to D-Modules<br />
| bgcolor="#BCE2FE" |On the basics of the theory of D-Modules and how it gets used.<br />
|-<br />
| bgcolor="#E0E0E0" | December 13<br />
| bgcolor="#C6D46E" | Maya Banks<br />
| bgcolor="#BCE2FE" | Intro to weighted projective space<br />
| bgcolor="#BCE2FE" |<br />
|}<br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023] <br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022] [https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022] <br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Fall_2023&diff=25688Directed Reading Program Fall 20232023-12-05T22:26:58Z<p>Jcobb2: /* Presentation Schedule */</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, December 6th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are closed.<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
{| class="wikitable"<br />
|+Fall 2023 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Analysis On Graphs<br />
|We will study analysis on graphs. More precisely, we will read the book ''Introduction to Analysis on Graphs'' by Alexander Grigor'yan. The purpose of the book is to provide an introduction to the subject of the discrete Laplace operator on locally finite graphs. Analysis on graphs is a subject studies classical calculus and differential equations on discrete objects such as graphs. It has connections with many other important areas in math and outside of math. <br />
|Students should be familiar with basic calculus (221, 222 and 234) and linear algebra. Analysis courses such as 521 and 522 or basic probability theory are helpful.<br />
|-<br />
|Analysis, Geometry, and Combinatorics<br />
|I am very flexible and happy to work with your backgrounds and interests. A few things I've thought about are:<br />
<br />
- Looking at Guth's book "Polynomial Method's in Combinatorics", hopefully culminating in understanding the proof of the finite field Kakeya conjecture. <br />
<br />
- Measure theory - we'll start with Stein & Shakarchi's book, depending on how that goes, we could move on to Frank Morgan's "Geometric Measure Theory: A Beginner’s Guide" for a bit of geometric measure theory.<br />
<br />
- Laszlo Lovasz's book "Combinatorial Problems and Exercises". The name is pretty self-explanatory - this books balances more towards problems and less towards theory, but won't require much background.<br />
<br />
- Spivak's book "Calculus on manifolds". This isn't your usual calculus book - it will introduce differential forms, which are very useful in geometry and analysis. <br />
|-<br />
|Fractal geometry<br />
|In recent years, a surprising connection between two seemingly unrelated branches of math has emerged. Fractal dimension is a notion of size for sets which, unlike how we normally think about dimension, is not necessarily an integer (e.g. the rough shape of a coastline, the branching of a bolt of lightning, or the chaotic movement of a stock's price have non-integer dimension). Kolmogorov complexity, which measures how much information a string contains, can be applied to characterize some types of fractal dimension. This connection has already yielded impressive new results about fractal sets. <br />
In this DRP, we will start by understanding notions of fractal dimension and the definition/properties of Kolmogorov complexity. Then, we'll bridge the gap between the two via "effective" dimension. Effective dimension gives rise to elegant characterizations of both Hausdorff and packing dimension via the recently proven point-to-set principle, which we will study. Finally, we'll see some applications of this alternative definition, which makes it one of the most powerful new tools in fractal geometry. <br />
|I would like students who have taken 521-522. But I'm flexible and happy to find something which you feel ready for.<br />
|-<br />
|Number theory and Partition Theory<br />
|We will investigate modular forms with a view towards algebraic combinatorics and number theory. In this project, we will first read about the interesting connections of modular forms and number theory/arithmetic geometry, with a focus on the theory of theta functions and elliptic curves. We will then transition to a more concrete application of modular forms via partition theory. In particular, we'll cover both analytic and combinatorial techniques, such as the circle method and enumerative combinatorics. We may also dive into more modern applications such as mock theta functions. Depending on participant interest this may turn into a research project based on prior work of the mentor on generalizing the Rogers-Ramanujan identities in partition theory. <br />
|Students should have completed a semester of algebra (541) and be familiar with proofs. Familiarity with complex analysis will be useful though not required. Coding knowledge with python would also be useful. <br />
|-<br />
|Measure Theory<br />
|Euclidean space may seem simple enough, but it contains many complicated subsets with highly counterintuitive properties. Throughout the semester, we'll consider a number of examples of such subsets, including the standard Cantor set, fat and thin Cantor sets, Vitali sets, "large" meager sets, purely unrectifiable sets, Kakeya sets, Nikodym sets, and many more. Readings will be provided and will come from a variety of sources, <br />
|Students should either have taken 521 or currently be enrolled in it. <br />
|-<br />
|Basics of D-modules<br />
|In this project, students will be introduced to D-modules, which allow us to think about ideas from calculus, such as derivatives and differential equations, in an algebraic context. The topics covered will include the Weyl algebra, the Jacobian conjecture, rings of differential operators, modules over the Weyl algebra, and differential equations. The text we will use is "A Primer of Algebraic D-modules" by S.C. Coutinho.<br />
|The prerequisite is math 541 or an equivalent: rings, ideals, homomorphisms, polynomial rings, and abstract vector spaces. A basic knowledge of modules is necessary, but this can be introduced at the beginning of the project.<br />
|-<br />
|Commutative Algebra<br />
|Ideals, Varieties, and Algorithms (Chapters 1-2) with a view toward algebraic geometry.Students are expected to give "mini-talks" on the board for the section we read that week. <br />
|Some knowledge of abstract algebra but not much else.<br />
|-<br />
|Computability Theory, or, Algebra<br />
|1, Computability Theory: we will focus on computability theory, complexity theory, and cryptography. There is a book called Computational Complexity: A Moder Approach, and we can pay more attention to Non-determinism and NP Completeness. <br />
<br />
2, Algebra: we will focus on Linear Representations of Finite Groups. It is also the name of a book which describes the correspondence, due to Frobenius, between linear representations and characters. The book says this is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics and have tried to give proofs as elementary as possible, using only the definition of a group and the rudiments of linear algebra.<br />
|Strong abilities of Analysis and Discrete Mathematics (including Algebra, etc)<br />
|-<br />
|Machine Learning<br />
| In this project, students will read/watch parts of the "Practical Deep Learning for Coders" course of fast.ai, a deep learning library that aims to make deep learning as accessible as possible, with the aim of training a basic machine learning model of their own design. In parallel, the students will also develop the skills for some software development practices, such as unit testing, documentation, and key bindings.<br />
|Calculus, Linear Algebra, and basic programming experience (preferably including Python) are required. I would also like the students to be mostly independent as designing their own machine learning model is a goal for this project (although this goal is not a hard requirement) and as I might be away for some weeks during the semester.<br />
|-<br />
|Dynamics (Analysis/Geometry)<br />
|Ergodic theory studies dynamical systems (we can think of this as a repeated action) and their statistical properties (i.e. time averages). For example, consider a circle and pick a point and an angle. Now our action will be repeatedly rotating the point by the chosen angle. Now if we do this action repeatedly for a long time, what will the resulting orbit of the point be? Will it miss part of the circle? Go everywhere? Go everywhere equally often? If we choose an irrational angle the last is true and we call the system ergodic. Ergodic theory is concerned with the study of these systems. While we won’t directly study them, ergodic theory has applications in many other fields -- including number theory, harmonic analysis, probability, and mathematical physics -- making it an incredibly exciting multi-disciplinary area to study. Our plan will be to first spend some time reviewing measure theory, then look at some examples and define ergodicity rigorously. After that we will spend some time studying the various ergodic theorems. If time allows we will extend our study to mixing and entropy.<br />
|The Real Analysis sequence (or equivalent) is required. Having seen some measure theory will be extremely helpful though we will spend the first week or two reviewing this topic. Any geometry/topology is useful but not at all required.<br />
|}<br />
<br />
== Presentation Schedule ==<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|+Room 1 (Engineering Hall 3349)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:30-3:45<br />
| bgcolor="#C6D46E" | Erkin Delic<br />
| bgcolor="#BCE2FE" | Intro to D-modules<br />
|-<br />
| bgcolor="#E0E0E0" | 3:45-4:00<br />
| bgcolor="#C6D46E" | Yikai Zhang & Beining Mu<br />
| bgcolor="#BCE2FE" | Computability<br />
|-<br />
| bgcolor="#E0E0E0" | 4:00-4:45<br />
| bgcolor="#C6D46E" | Aidin Simkin, Yifan Yang, Sena Witzeling<br />
| bgcolor="#BCE2FE" | Several Strange Cantor Sets<br />
|-<br />
| bgcolor="#E0E0E0" | 4:45-5:00<br />
| bgcolor="#C6D46E" | Yancheng Zhu<br />
| bgcolor="#BCE2FE" | FastAi in NLP<br />
|-<br />
| bgcolor="#E0E0E0" | 5:00-5:15<br />
| bgcolor="#C6D46E" | Shi Kaiwen<br />
| bgcolor="#BCE2FE" | Machine learning application in stock index prediction<br />
|-<br />
| bgcolor="#E0E0E0" | 5:15-5:30<br />
| bgcolor="#C6D46E" | Hannah Wang<br />
| bgcolor="#BCE2FE" | Trained model for predicting the insurance price<br />
|}<br />
</center><br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|+Room 2 (Engineering Hall 3418)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:30-4:00 <br />
| bgcolor="#C6D46E" | Aiden Styers, Rui Yu, Yizhou Qian & Anvith Aravati<br />
| bgcolor="#BCE2FE" | Laplace Operator on Graphs<br />
|-<br />
| bgcolor="#E0E0E0" | 4:30-5:00<br />
| bgcolor="#C6D46E" | Benjamin Braiman & Ruoyu Men<br />
| bgcolor="#BCE2FE" | Ergodic Theory<br />
|-<br />
| bgcolor="#E0E0E0" | 5:00-5:15<br />
| bgcolor="#C6D46E" | David Jiang<br />
| bgcolor="#BCE2FE" | Ramanujan Partition Identities<br />
|}<br />
</center></div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Fall_2023&diff=25687Directed Reading Program Fall 20232023-12-05T22:26:45Z<p>Jcobb2: /* Presentation Schedule */</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, December 6th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are closed.<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
{| class="wikitable"<br />
|+Fall 2023 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Analysis On Graphs<br />
|We will study analysis on graphs. More precisely, we will read the book ''Introduction to Analysis on Graphs'' by Alexander Grigor'yan. The purpose of the book is to provide an introduction to the subject of the discrete Laplace operator on locally finite graphs. Analysis on graphs is a subject studies classical calculus and differential equations on discrete objects such as graphs. It has connections with many other important areas in math and outside of math. <br />
|Students should be familiar with basic calculus (221, 222 and 234) and linear algebra. Analysis courses such as 521 and 522 or basic probability theory are helpful.<br />
|-<br />
|Analysis, Geometry, and Combinatorics<br />
|I am very flexible and happy to work with your backgrounds and interests. A few things I've thought about are:<br />
<br />
- Looking at Guth's book "Polynomial Method's in Combinatorics", hopefully culminating in understanding the proof of the finite field Kakeya conjecture. <br />
<br />
- Measure theory - we'll start with Stein & Shakarchi's book, depending on how that goes, we could move on to Frank Morgan's "Geometric Measure Theory: A Beginner’s Guide" for a bit of geometric measure theory.<br />
<br />
- Laszlo Lovasz's book "Combinatorial Problems and Exercises". The name is pretty self-explanatory - this books balances more towards problems and less towards theory, but won't require much background.<br />
<br />
- Spivak's book "Calculus on manifolds". This isn't your usual calculus book - it will introduce differential forms, which are very useful in geometry and analysis. <br />
|-<br />
|Fractal geometry<br />
|In recent years, a surprising connection between two seemingly unrelated branches of math has emerged. Fractal dimension is a notion of size for sets which, unlike how we normally think about dimension, is not necessarily an integer (e.g. the rough shape of a coastline, the branching of a bolt of lightning, or the chaotic movement of a stock's price have non-integer dimension). Kolmogorov complexity, which measures how much information a string contains, can be applied to characterize some types of fractal dimension. This connection has already yielded impressive new results about fractal sets. <br />
In this DRP, we will start by understanding notions of fractal dimension and the definition/properties of Kolmogorov complexity. Then, we'll bridge the gap between the two via "effective" dimension. Effective dimension gives rise to elegant characterizations of both Hausdorff and packing dimension via the recently proven point-to-set principle, which we will study. Finally, we'll see some applications of this alternative definition, which makes it one of the most powerful new tools in fractal geometry. <br />
|I would like students who have taken 521-522. But I'm flexible and happy to find something which you feel ready for.<br />
|-<br />
|Number theory and Partition Theory<br />
|We will investigate modular forms with a view towards algebraic combinatorics and number theory. In this project, we will first read about the interesting connections of modular forms and number theory/arithmetic geometry, with a focus on the theory of theta functions and elliptic curves. We will then transition to a more concrete application of modular forms via partition theory. In particular, we'll cover both analytic and combinatorial techniques, such as the circle method and enumerative combinatorics. We may also dive into more modern applications such as mock theta functions. Depending on participant interest this may turn into a research project based on prior work of the mentor on generalizing the Rogers-Ramanujan identities in partition theory. <br />
|Students should have completed a semester of algebra (541) and be familiar with proofs. Familiarity with complex analysis will be useful though not required. Coding knowledge with python would also be useful. <br />
|-<br />
|Measure Theory<br />
|Euclidean space may seem simple enough, but it contains many complicated subsets with highly counterintuitive properties. Throughout the semester, we'll consider a number of examples of such subsets, including the standard Cantor set, fat and thin Cantor sets, Vitali sets, "large" meager sets, purely unrectifiable sets, Kakeya sets, Nikodym sets, and many more. Readings will be provided and will come from a variety of sources, <br />
|Students should either have taken 521 or currently be enrolled in it. <br />
|-<br />
|Basics of D-modules<br />
|In this project, students will be introduced to D-modules, which allow us to think about ideas from calculus, such as derivatives and differential equations, in an algebraic context. The topics covered will include the Weyl algebra, the Jacobian conjecture, rings of differential operators, modules over the Weyl algebra, and differential equations. The text we will use is "A Primer of Algebraic D-modules" by S.C. Coutinho.<br />
|The prerequisite is math 541 or an equivalent: rings, ideals, homomorphisms, polynomial rings, and abstract vector spaces. A basic knowledge of modules is necessary, but this can be introduced at the beginning of the project.<br />
|-<br />
|Commutative Algebra<br />
|Ideals, Varieties, and Algorithms (Chapters 1-2) with a view toward algebraic geometry.Students are expected to give "mini-talks" on the board for the section we read that week. <br />
|Some knowledge of abstract algebra but not much else.<br />
|-<br />
|Computability Theory, or, Algebra<br />
|1, Computability Theory: we will focus on computability theory, complexity theory, and cryptography. There is a book called Computational Complexity: A Moder Approach, and we can pay more attention to Non-determinism and NP Completeness. <br />
<br />
2, Algebra: we will focus on Linear Representations of Finite Groups. It is also the name of a book which describes the correspondence, due to Frobenius, between linear representations and characters. The book says this is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics and have tried to give proofs as elementary as possible, using only the definition of a group and the rudiments of linear algebra.<br />
|Strong abilities of Analysis and Discrete Mathematics (including Algebra, etc)<br />
|-<br />
|Machine Learning<br />
| In this project, students will read/watch parts of the "Practical Deep Learning for Coders" course of fast.ai, a deep learning library that aims to make deep learning as accessible as possible, with the aim of training a basic machine learning model of their own design. In parallel, the students will also develop the skills for some software development practices, such as unit testing, documentation, and key bindings.<br />
|Calculus, Linear Algebra, and basic programming experience (preferably including Python) are required. I would also like the students to be mostly independent as designing their own machine learning model is a goal for this project (although this goal is not a hard requirement) and as I might be away for some weeks during the semester.<br />
|-<br />
|Dynamics (Analysis/Geometry)<br />
|Ergodic theory studies dynamical systems (we can think of this as a repeated action) and their statistical properties (i.e. time averages). For example, consider a circle and pick a point and an angle. Now our action will be repeatedly rotating the point by the chosen angle. Now if we do this action repeatedly for a long time, what will the resulting orbit of the point be? Will it miss part of the circle? Go everywhere? Go everywhere equally often? If we choose an irrational angle the last is true and we call the system ergodic. Ergodic theory is concerned with the study of these systems. While we won’t directly study them, ergodic theory has applications in many other fields -- including number theory, harmonic analysis, probability, and mathematical physics -- making it an incredibly exciting multi-disciplinary area to study. Our plan will be to first spend some time reviewing measure theory, then look at some examples and define ergodicity rigorously. After that we will spend some time studying the various ergodic theorems. If time allows we will extend our study to mixing and entropy.<br />
|The Real Analysis sequence (or equivalent) is required. Having seen some measure theory will be extremely helpful though we will spend the first week or two reviewing this topic. Any geometry/topology is useful but not at all required.<br />
|}<br />
<br />
== Presentation Schedule ==<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|+Room 1 (Engineering Hall 3349)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:45-4:00<br />
| bgcolor="#C6D46E" | Erkin Delic<br />
| bgcolor="#BCE2FE" | Intro to D-modules<br />
|-<br />
| bgcolor="#E0E0E0" | 3:45-4:00<br />
| bgcolor="#C6D46E" | Yikai Zhang & Beining Mu<br />
| bgcolor="#BCE2FE" | Computability<br />
|-<br />
| bgcolor="#E0E0E0" | 4:00-4:45<br />
| bgcolor="#C6D46E" | Aidin Simkin, Yifan Yang, Sena Witzeling<br />
| bgcolor="#BCE2FE" | Several Strange Cantor Sets<br />
|-<br />
| bgcolor="#E0E0E0" | 4:45-5:00<br />
| bgcolor="#C6D46E" | Yancheng Zhu<br />
| bgcolor="#BCE2FE" | FastAi in NLP<br />
|-<br />
| bgcolor="#E0E0E0" | 5:00-5:15<br />
| bgcolor="#C6D46E" | Shi Kaiwen<br />
| bgcolor="#BCE2FE" | Machine learning application in stock index prediction<br />
|-<br />
| bgcolor="#E0E0E0" | 5:15-5:30<br />
| bgcolor="#C6D46E" | Hannah Wang<br />
| bgcolor="#BCE2FE" | Trained model for predicting the insurance price<br />
|}<br />
</center><br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|+Room 2 (Engineering Hall 3418)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:30-4:00 <br />
| bgcolor="#C6D46E" | Aiden Styers, Rui Yu, Yizhou Qian & Anvith Aravati<br />
| bgcolor="#BCE2FE" | Laplace Operator on Graphs<br />
|-<br />
| bgcolor="#E0E0E0" | 4:30-5:00<br />
| bgcolor="#C6D46E" | Benjamin Braiman & Ruoyu Men<br />
| bgcolor="#BCE2FE" | Ergodic Theory<br />
|-<br />
| bgcolor="#E0E0E0" | 5:00-5:15<br />
| bgcolor="#C6D46E" | David Jiang<br />
| bgcolor="#BCE2FE" | Ramanujan Partition Identities<br />
|}<br />
</center></div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Fall_2023&diff=25685Directed Reading Program Fall 20232023-12-05T15:54:46Z<p>Jcobb2: /* Presentation Schedule */</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, December 6th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are closed.<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
{| class="wikitable"<br />
|+Fall 2023 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Analysis On Graphs<br />
|We will study analysis on graphs. More precisely, we will read the book ''Introduction to Analysis on Graphs'' by Alexander Grigor'yan. The purpose of the book is to provide an introduction to the subject of the discrete Laplace operator on locally finite graphs. Analysis on graphs is a subject studies classical calculus and differential equations on discrete objects such as graphs. It has connections with many other important areas in math and outside of math. <br />
|Students should be familiar with basic calculus (221, 222 and 234) and linear algebra. Analysis courses such as 521 and 522 or basic probability theory are helpful.<br />
|-<br />
|Analysis, Geometry, and Combinatorics<br />
|I am very flexible and happy to work with your backgrounds and interests. A few things I've thought about are:<br />
<br />
- Looking at Guth's book "Polynomial Method's in Combinatorics", hopefully culminating in understanding the proof of the finite field Kakeya conjecture. <br />
<br />
- Measure theory - we'll start with Stein & Shakarchi's book, depending on how that goes, we could move on to Frank Morgan's "Geometric Measure Theory: A Beginner’s Guide" for a bit of geometric measure theory.<br />
<br />
- Laszlo Lovasz's book "Combinatorial Problems and Exercises". The name is pretty self-explanatory - this books balances more towards problems and less towards theory, but won't require much background.<br />
<br />
- Spivak's book "Calculus on manifolds". This isn't your usual calculus book - it will introduce differential forms, which are very useful in geometry and analysis. <br />
|-<br />
|Fractal geometry<br />
|In recent years, a surprising connection between two seemingly unrelated branches of math has emerged. Fractal dimension is a notion of size for sets which, unlike how we normally think about dimension, is not necessarily an integer (e.g. the rough shape of a coastline, the branching of a bolt of lightning, or the chaotic movement of a stock's price have non-integer dimension). Kolmogorov complexity, which measures how much information a string contains, can be applied to characterize some types of fractal dimension. This connection has already yielded impressive new results about fractal sets. <br />
In this DRP, we will start by understanding notions of fractal dimension and the definition/properties of Kolmogorov complexity. Then, we'll bridge the gap between the two via "effective" dimension. Effective dimension gives rise to elegant characterizations of both Hausdorff and packing dimension via the recently proven point-to-set principle, which we will study. Finally, we'll see some applications of this alternative definition, which makes it one of the most powerful new tools in fractal geometry. <br />
|I would like students who have taken 521-522. But I'm flexible and happy to find something which you feel ready for.<br />
|-<br />
|Number theory and Partition Theory<br />
|We will investigate modular forms with a view towards algebraic combinatorics and number theory. In this project, we will first read about the interesting connections of modular forms and number theory/arithmetic geometry, with a focus on the theory of theta functions and elliptic curves. We will then transition to a more concrete application of modular forms via partition theory. In particular, we'll cover both analytic and combinatorial techniques, such as the circle method and enumerative combinatorics. We may also dive into more modern applications such as mock theta functions. Depending on participant interest this may turn into a research project based on prior work of the mentor on generalizing the Rogers-Ramanujan identities in partition theory. <br />
|Students should have completed a semester of algebra (541) and be familiar with proofs. Familiarity with complex analysis will be useful though not required. Coding knowledge with python would also be useful. <br />
|-<br />
|Measure Theory<br />
|Euclidean space may seem simple enough, but it contains many complicated subsets with highly counterintuitive properties. Throughout the semester, we'll consider a number of examples of such subsets, including the standard Cantor set, fat and thin Cantor sets, Vitali sets, "large" meager sets, purely unrectifiable sets, Kakeya sets, Nikodym sets, and many more. Readings will be provided and will come from a variety of sources, <br />
|Students should either have taken 521 or currently be enrolled in it. <br />
|-<br />
|Basics of D-modules<br />
|In this project, students will be introduced to D-modules, which allow us to think about ideas from calculus, such as derivatives and differential equations, in an algebraic context. The topics covered will include the Weyl algebra, the Jacobian conjecture, rings of differential operators, modules over the Weyl algebra, and differential equations. The text we will use is "A Primer of Algebraic D-modules" by S.C. Coutinho.<br />
|The prerequisite is math 541 or an equivalent: rings, ideals, homomorphisms, polynomial rings, and abstract vector spaces. A basic knowledge of modules is necessary, but this can be introduced at the beginning of the project.<br />
|-<br />
|Commutative Algebra<br />
|Ideals, Varieties, and Algorithms (Chapters 1-2) with a view toward algebraic geometry.Students are expected to give "mini-talks" on the board for the section we read that week. <br />
|Some knowledge of abstract algebra but not much else.<br />
|-<br />
|Computability Theory, or, Algebra<br />
|1, Computability Theory: we will focus on computability theory, complexity theory, and cryptography. There is a book called Computational Complexity: A Moder Approach, and we can pay more attention to Non-determinism and NP Completeness. <br />
<br />
2, Algebra: we will focus on Linear Representations of Finite Groups. It is also the name of a book which describes the correspondence, due to Frobenius, between linear representations and characters. The book says this is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics and have tried to give proofs as elementary as possible, using only the definition of a group and the rudiments of linear algebra.<br />
|Strong abilities of Analysis and Discrete Mathematics (including Algebra, etc)<br />
|-<br />
|Machine Learning<br />
| In this project, students will read/watch parts of the "Practical Deep Learning for Coders" course of fast.ai, a deep learning library that aims to make deep learning as accessible as possible, with the aim of training a basic machine learning model of their own design. In parallel, the students will also develop the skills for some software development practices, such as unit testing, documentation, and key bindings.<br />
|Calculus, Linear Algebra, and basic programming experience (preferably including Python) are required. I would also like the students to be mostly independent as designing their own machine learning model is a goal for this project (although this goal is not a hard requirement) and as I might be away for some weeks during the semester.<br />
|-<br />
|Dynamics (Analysis/Geometry)<br />
|Ergodic theory studies dynamical systems (we can think of this as a repeated action) and their statistical properties (i.e. time averages). For example, consider a circle and pick a point and an angle. Now our action will be repeatedly rotating the point by the chosen angle. Now if we do this action repeatedly for a long time, what will the resulting orbit of the point be? Will it miss part of the circle? Go everywhere? Go everywhere equally often? If we choose an irrational angle the last is true and we call the system ergodic. Ergodic theory is concerned with the study of these systems. While we won’t directly study them, ergodic theory has applications in many other fields -- including number theory, harmonic analysis, probability, and mathematical physics -- making it an incredibly exciting multi-disciplinary area to study. Our plan will be to first spend some time reviewing measure theory, then look at some examples and define ergodicity rigorously. After that we will spend some time studying the various ergodic theorems. If time allows we will extend our study to mixing and entropy.<br />
|The Real Analysis sequence (or equivalent) is required. Having seen some measure theory will be extremely helpful though we will spend the first week or two reviewing this topic. Any geometry/topology is useful but not at all required.<br />
|}<br />
<br />
== Presentation Schedule ==<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|+Room 1 (Engineering Hall 3349)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:45-4:00<br />
| bgcolor="#C6D46E" | Yikai Zhang & Beining Mu<br />
| bgcolor="#BCE2FE" | Computability<br />
|-<br />
| bgcolor="#E0E0E0" | 4:00-4:45<br />
| bgcolor="#C6D46E" | Aidin Simkin, Yifan Yang, Sena Witzeling<br />
| bgcolor="#BCE2FE" | Several Strange Cantor Sets<br />
|-<br />
| bgcolor="#E0E0E0" | 4:45-5:00<br />
| bgcolor="#C6D46E" | Yancheng Zhu<br />
| bgcolor="#BCE2FE" | FastAi in NLP<br />
|-<br />
| bgcolor="#E0E0E0" | 5:00-5:15<br />
| bgcolor="#C6D46E" | Shi Kaiwen<br />
| bgcolor="#BCE2FE" | Machine learning application in stock index prediction<br />
|-<br />
| bgcolor="#E0E0E0" | 5:15-5:30<br />
| bgcolor="#C6D46E" | Hannah Wang<br />
| bgcolor="#BCE2FE" | Trained model for predicting the insurance price<br />
|}<br />
</center><br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|+Room 2 (Engineering Hall 3418)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:30-4:00 <br />
| bgcolor="#C6D46E" | Aiden Styers, Rui Yu, Yizhou Qian & Anvith Aravati<br />
| bgcolor="#BCE2FE" | Laplace Operator on Graphs<br />
|-<br />
| bgcolor="#E0E0E0" | 4:30-5:00<br />
| bgcolor="#C6D46E" | Benjamin Braiman & Ruoyu Men<br />
| bgcolor="#BCE2FE" | Ergodic Theory<br />
|-<br />
| bgcolor="#E0E0E0" | 5:00-5:15<br />
| bgcolor="#C6D46E" | David Jiang<br />
| bgcolor="#BCE2FE" | Ramanujan Partition Identities<br />
|}<br />
</center></div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Fall_2023&diff=25674Directed Reading Program Fall 20232023-11-29T23:40:37Z<p>Jcobb2: /* Presentation Schedule */</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, December 6th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are closed.<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
{| class="wikitable"<br />
|+Fall 2023 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Analysis On Graphs<br />
|We will study analysis on graphs. More precisely, we will read the book ''Introduction to Analysis on Graphs'' by Alexander Grigor'yan. The purpose of the book is to provide an introduction to the subject of the discrete Laplace operator on locally finite graphs. Analysis on graphs is a subject studies classical calculus and differential equations on discrete objects such as graphs. It has connections with many other important areas in math and outside of math. <br />
|Students should be familiar with basic calculus (221, 222 and 234) and linear algebra. Analysis courses such as 521 and 522 or basic probability theory are helpful.<br />
|-<br />
|Analysis, Geometry, and Combinatorics<br />
|I am very flexible and happy to work with your backgrounds and interests. A few things I've thought about are:<br />
<br />
- Looking at Guth's book "Polynomial Method's in Combinatorics", hopefully culminating in understanding the proof of the finite field Kakeya conjecture. <br />
<br />
- Measure theory - we'll start with Stein & Shakarchi's book, depending on how that goes, we could move on to Frank Morgan's "Geometric Measure Theory: A Beginner’s Guide" for a bit of geometric measure theory.<br />
<br />
- Laszlo Lovasz's book "Combinatorial Problems and Exercises". The name is pretty self-explanatory - this books balances more towards problems and less towards theory, but won't require much background.<br />
<br />
- Spivak's book "Calculus on manifolds". This isn't your usual calculus book - it will introduce differential forms, which are very useful in geometry and analysis. <br />
|-<br />
|Fractal geometry<br />
|In recent years, a surprising connection between two seemingly unrelated branches of math has emerged. Fractal dimension is a notion of size for sets which, unlike how we normally think about dimension, is not necessarily an integer (e.g. the rough shape of a coastline, the branching of a bolt of lightning, or the chaotic movement of a stock's price have non-integer dimension). Kolmogorov complexity, which measures how much information a string contains, can be applied to characterize some types of fractal dimension. This connection has already yielded impressive new results about fractal sets. <br />
In this DRP, we will start by understanding notions of fractal dimension and the definition/properties of Kolmogorov complexity. Then, we'll bridge the gap between the two via "effective" dimension. Effective dimension gives rise to elegant characterizations of both Hausdorff and packing dimension via the recently proven point-to-set principle, which we will study. Finally, we'll see some applications of this alternative definition, which makes it one of the most powerful new tools in fractal geometry. <br />
|I would like students who have taken 521-522. But I'm flexible and happy to find something which you feel ready for.<br />
|-<br />
|Number theory and Partition Theory<br />
|We will investigate modular forms with a view towards algebraic combinatorics and number theory. In this project, we will first read about the interesting connections of modular forms and number theory/arithmetic geometry, with a focus on the theory of theta functions and elliptic curves. We will then transition to a more concrete application of modular forms via partition theory. In particular, we'll cover both analytic and combinatorial techniques, such as the circle method and enumerative combinatorics. We may also dive into more modern applications such as mock theta functions. Depending on participant interest this may turn into a research project based on prior work of the mentor on generalizing the Rogers-Ramanujan identities in partition theory. <br />
|Students should have completed a semester of algebra (541) and be familiar with proofs. Familiarity with complex analysis will be useful though not required. Coding knowledge with python would also be useful. <br />
|-<br />
|Measure Theory<br />
|Euclidean space may seem simple enough, but it contains many complicated subsets with highly counterintuitive properties. Throughout the semester, we'll consider a number of examples of such subsets, including the standard Cantor set, fat and thin Cantor sets, Vitali sets, "large" meager sets, purely unrectifiable sets, Kakeya sets, Nikodym sets, and many more. Readings will be provided and will come from a variety of sources, <br />
|Students should either have taken 521 or currently be enrolled in it. <br />
|-<br />
|Basics of D-modules<br />
|In this project, students will be introduced to D-modules, which allow us to think about ideas from calculus, such as derivatives and differential equations, in an algebraic context. The topics covered will include the Weyl algebra, the Jacobian conjecture, rings of differential operators, modules over the Weyl algebra, and differential equations. The text we will use is "A Primer of Algebraic D-modules" by S.C. Coutinho.<br />
|The prerequisite is math 541 or an equivalent: rings, ideals, homomorphisms, polynomial rings, and abstract vector spaces. A basic knowledge of modules is necessary, but this can be introduced at the beginning of the project.<br />
|-<br />
|Commutative Algebra<br />
|Ideals, Varieties, and Algorithms (Chapters 1-2) with a view toward algebraic geometry.Students are expected to give "mini-talks" on the board for the section we read that week. <br />
|Some knowledge of abstract algebra but not much else.<br />
|-<br />
|Computability Theory, or, Algebra<br />
|1, Computability Theory: we will focus on computability theory, complexity theory, and cryptography. There is a book called Computational Complexity: A Moder Approach, and we can pay more attention to Non-determinism and NP Completeness. <br />
<br />
2, Algebra: we will focus on Linear Representations of Finite Groups. It is also the name of a book which describes the correspondence, due to Frobenius, between linear representations and characters. The book says this is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics and have tried to give proofs as elementary as possible, using only the definition of a group and the rudiments of linear algebra.<br />
|Strong abilities of Analysis and Discrete Mathematics (including Algebra, etc)<br />
|-<br />
|Machine Learning<br />
| In this project, students will read/watch parts of the "Practical Deep Learning for Coders" course of fast.ai, a deep learning library that aims to make deep learning as accessible as possible, with the aim of training a basic machine learning model of their own design. In parallel, the students will also develop the skills for some software development practices, such as unit testing, documentation, and key bindings.<br />
|Calculus, Linear Algebra, and basic programming experience (preferably including Python) are required. I would also like the students to be mostly independent as designing their own machine learning model is a goal for this project (although this goal is not a hard requirement) and as I might be away for some weeks during the semester.<br />
|-<br />
|Dynamics (Analysis/Geometry)<br />
|Ergodic theory studies dynamical systems (we can think of this as a repeated action) and their statistical properties (i.e. time averages). For example, consider a circle and pick a point and an angle. Now our action will be repeatedly rotating the point by the chosen angle. Now if we do this action repeatedly for a long time, what will the resulting orbit of the point be? Will it miss part of the circle? Go everywhere? Go everywhere equally often? If we choose an irrational angle the last is true and we call the system ergodic. Ergodic theory is concerned with the study of these systems. While we won’t directly study them, ergodic theory has applications in many other fields -- including number theory, harmonic analysis, probability, and mathematical physics -- making it an incredibly exciting multi-disciplinary area to study. Our plan will be to first spend some time reviewing measure theory, then look at some examples and define ergodicity rigorously. After that we will spend some time studying the various ergodic theorems. If time allows we will extend our study to mixing and entropy.<br />
|The Real Analysis sequence (or equivalent) is required. Having seen some measure theory will be extremely helpful though we will spend the first week or two reviewing this topic. Any geometry/topology is useful but not at all required.<br />
|}<br />
<br />
== Presentation Schedule ==<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|+Room 1 (Van Vleck B329)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:45-4:00<br />
| bgcolor="#C6D46E" | Yikai Zhang & Beining Mu<br />
| bgcolor="#BCE2FE" | Computability<br />
|-<br />
| bgcolor="#E0E0E0" | 4:00-4:45<br />
| bgcolor="#C6D46E" | Aidin Simkin, Yifan Yang, Sena Witzeling<br />
| bgcolor="#BCE2FE" | Several Strange Cantor Sets<br />
|-<br />
| bgcolor="#E0E0E0" | 4:45-5:00<br />
| bgcolor="#C6D46E" | Yancheng Zhu<br />
| bgcolor="#BCE2FE" | FastAi in NLP<br />
|-<br />
| bgcolor="#E0E0E0" | 5:00-5:15<br />
| bgcolor="#C6D46E" | Shi Kaiwen<br />
| bgcolor="#BCE2FE" | Machine learning application in stock index prediction<br />
|-<br />
| bgcolor="#E0E0E0" | 5:15-5:30<br />
| bgcolor="#C6D46E" | Hannah Wang<br />
| bgcolor="#BCE2FE" | Trained model for predicting the insurance price<br />
|}<br />
</center><br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|+Room 2 (Van Vleck B333)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:30-4:00 <br />
| bgcolor="#C6D46E" | Aiden Styers, Rui Yu, Yizhou Qian & Anvith Aravati<br />
| bgcolor="#BCE2FE" | Laplace Operator on Graphs<br />
|-<br />
| bgcolor="#E0E0E0" | 4:30-5:00<br />
| bgcolor="#C6D46E" | Benjamin Braiman & Ruoyu Men<br />
| bgcolor="#BCE2FE" | Ergodic Theory<br />
|-<br />
| bgcolor="#E0E0E0" | 5:00-5:15<br />
| bgcolor="#C6D46E" | David Jiang<br />
| bgcolor="#BCE2FE" | Ramanujan Partition Identities<br />
|}<br />
</center></div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Fall_2023&diff=25659Directed Reading Program Fall 20232023-11-28T17:42:36Z<p>Jcobb2: /* Presentation Schedule */</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, December 6th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are closed.<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
{| class="wikitable"<br />
|+Fall 2023 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Analysis On Graphs<br />
|We will study analysis on graphs. More precisely, we will read the book ''Introduction to Analysis on Graphs'' by Alexander Grigor'yan. The purpose of the book is to provide an introduction to the subject of the discrete Laplace operator on locally finite graphs. Analysis on graphs is a subject studies classical calculus and differential equations on discrete objects such as graphs. It has connections with many other important areas in math and outside of math. <br />
|Students should be familiar with basic calculus (221, 222 and 234) and linear algebra. Analysis courses such as 521 and 522 or basic probability theory are helpful.<br />
|-<br />
|Analysis, Geometry, and Combinatorics<br />
|I am very flexible and happy to work with your backgrounds and interests. A few things I've thought about are:<br />
<br />
- Looking at Guth's book "Polynomial Method's in Combinatorics", hopefully culminating in understanding the proof of the finite field Kakeya conjecture. <br />
<br />
- Measure theory - we'll start with Stein & Shakarchi's book, depending on how that goes, we could move on to Frank Morgan's "Geometric Measure Theory: A Beginner’s Guide" for a bit of geometric measure theory.<br />
<br />
- Laszlo Lovasz's book "Combinatorial Problems and Exercises". The name is pretty self-explanatory - this books balances more towards problems and less towards theory, but won't require much background.<br />
<br />
- Spivak's book "Calculus on manifolds". This isn't your usual calculus book - it will introduce differential forms, which are very useful in geometry and analysis. <br />
|-<br />
|Fractal geometry<br />
|In recent years, a surprising connection between two seemingly unrelated branches of math has emerged. Fractal dimension is a notion of size for sets which, unlike how we normally think about dimension, is not necessarily an integer (e.g. the rough shape of a coastline, the branching of a bolt of lightning, or the chaotic movement of a stock's price have non-integer dimension). Kolmogorov complexity, which measures how much information a string contains, can be applied to characterize some types of fractal dimension. This connection has already yielded impressive new results about fractal sets. <br />
In this DRP, we will start by understanding notions of fractal dimension and the definition/properties of Kolmogorov complexity. Then, we'll bridge the gap between the two via "effective" dimension. Effective dimension gives rise to elegant characterizations of both Hausdorff and packing dimension via the recently proven point-to-set principle, which we will study. Finally, we'll see some applications of this alternative definition, which makes it one of the most powerful new tools in fractal geometry. <br />
|I would like students who have taken 521-522. But I'm flexible and happy to find something which you feel ready for.<br />
|-<br />
|Number theory and Partition Theory<br />
|We will investigate modular forms with a view towards algebraic combinatorics and number theory. In this project, we will first read about the interesting connections of modular forms and number theory/arithmetic geometry, with a focus on the theory of theta functions and elliptic curves. We will then transition to a more concrete application of modular forms via partition theory. In particular, we'll cover both analytic and combinatorial techniques, such as the circle method and enumerative combinatorics. We may also dive into more modern applications such as mock theta functions. Depending on participant interest this may turn into a research project based on prior work of the mentor on generalizing the Rogers-Ramanujan identities in partition theory. <br />
|Students should have completed a semester of algebra (541) and be familiar with proofs. Familiarity with complex analysis will be useful though not required. Coding knowledge with python would also be useful. <br />
|-<br />
|Measure Theory<br />
|Euclidean space may seem simple enough, but it contains many complicated subsets with highly counterintuitive properties. Throughout the semester, we'll consider a number of examples of such subsets, including the standard Cantor set, fat and thin Cantor sets, Vitali sets, "large" meager sets, purely unrectifiable sets, Kakeya sets, Nikodym sets, and many more. Readings will be provided and will come from a variety of sources, <br />
|Students should either have taken 521 or currently be enrolled in it. <br />
|-<br />
|Basics of D-modules<br />
|In this project, students will be introduced to D-modules, which allow us to think about ideas from calculus, such as derivatives and differential equations, in an algebraic context. The topics covered will include the Weyl algebra, the Jacobian conjecture, rings of differential operators, modules over the Weyl algebra, and differential equations. The text we will use is "A Primer of Algebraic D-modules" by S.C. Coutinho.<br />
|The prerequisite is math 541 or an equivalent: rings, ideals, homomorphisms, polynomial rings, and abstract vector spaces. A basic knowledge of modules is necessary, but this can be introduced at the beginning of the project.<br />
|-<br />
|Commutative Algebra<br />
|Ideals, Varieties, and Algorithms (Chapters 1-2) with a view toward algebraic geometry.Students are expected to give "mini-talks" on the board for the section we read that week. <br />
|Some knowledge of abstract algebra but not much else.<br />
|-<br />
|Computability Theory, or, Algebra<br />
|1, Computability Theory: we will focus on computability theory, complexity theory, and cryptography. There is a book called Computational Complexity: A Moder Approach, and we can pay more attention to Non-determinism and NP Completeness. <br />
<br />
2, Algebra: we will focus on Linear Representations of Finite Groups. It is also the name of a book which describes the correspondence, due to Frobenius, between linear representations and characters. The book says this is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics and have tried to give proofs as elementary as possible, using only the definition of a group and the rudiments of linear algebra.<br />
|Strong abilities of Analysis and Discrete Mathematics (including Algebra, etc)<br />
|-<br />
|Machine Learning<br />
| In this project, students will read/watch parts of the "Practical Deep Learning for Coders" course of fast.ai, a deep learning library that aims to make deep learning as accessible as possible, with the aim of training a basic machine learning model of their own design. In parallel, the students will also develop the skills for some software development practices, such as unit testing, documentation, and key bindings.<br />
|Calculus, Linear Algebra, and basic programming experience (preferably including Python) are required. I would also like the students to be mostly independent as designing their own machine learning model is a goal for this project (although this goal is not a hard requirement) and as I might be away for some weeks during the semester.<br />
|-<br />
|Dynamics (Analysis/Geometry)<br />
|Ergodic theory studies dynamical systems (we can think of this as a repeated action) and their statistical properties (i.e. time averages). For example, consider a circle and pick a point and an angle. Now our action will be repeatedly rotating the point by the chosen angle. Now if we do this action repeatedly for a long time, what will the resulting orbit of the point be? Will it miss part of the circle? Go everywhere? Go everywhere equally often? If we choose an irrational angle the last is true and we call the system ergodic. Ergodic theory is concerned with the study of these systems. While we won’t directly study them, ergodic theory has applications in many other fields -- including number theory, harmonic analysis, probability, and mathematical physics -- making it an incredibly exciting multi-disciplinary area to study. Our plan will be to first spend some time reviewing measure theory, then look at some examples and define ergodicity rigorously. After that we will spend some time studying the various ergodic theorems. If time allows we will extend our study to mixing and entropy.<br />
|The Real Analysis sequence (or equivalent) is required. Having seen some measure theory will be extremely helpful though we will spend the first week or two reviewing this topic. Any geometry/topology is useful but not at all required.<br />
|}<br />
<br />
== Presentation Schedule ==<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|+Room 1 (Van Vleck B329)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:45-4:00<br />
| bgcolor="#C6D46E" | Yikai Zhang & Beining Mu<br />
| bgcolor="#BCE2FE" | Computability<br />
|-<br />
| bgcolor="#E0E0E0" | 4:00-4:45<br />
| bgcolor="#C6D46E" | Aidin Simkin, Yifan Yang, Sena Witzeling<br />
| bgcolor="#BCE2FE" | Several Strange Cantor Sets<br />
|-<br />
| bgcolor="#E0E0E0" | 4:45-5:00<br />
| bgcolor="#C6D46E" | Yancheng Zhu<br />
| bgcolor="#BCE2FE" | FastAi in NLP<br />
|-<br />
| bgcolor="#E0E0E0" | 5:00-5:15<br />
| bgcolor="#C6D46E" | Shi Kaiwen<br />
| bgcolor="#BCE2FE" | Machine learning application in stock index prediction<br />
|-<br />
| bgcolor="#E0E0E0" | 5:15-5:30<br />
| bgcolor="#C6D46E" | Hannah Wang<br />
| bgcolor="#BCE2FE" | Trained model for predicting the insurance price<br />
|}<br />
</center><br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|+Room 2 (Van Vleck B333)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:30-4:00 <br />
| bgcolor="#C6D46E" | Aiden Styers, Rui Yu, Yizhou Qian & Anvith Aravati<br />
| bgcolor="#BCE2FE" | Laplace Operator on Graphs<br />
|-<br />
| bgcolor="#E0E0E0" | 4:45-5:00<br />
| bgcolor="#C6D46E" | Benjamin Braiman & Ruoyu Men<br />
| bgcolor="#BCE2FE" | Ergodic Theory<br />
|-<br />
| bgcolor="#E0E0E0" | 5:00-5:15<br />
| bgcolor="#C6D46E" | David Jiang<br />
| bgcolor="#BCE2FE" | Ramanujan Partition Identities<br />
|}<br />
</center></div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Fall_2023&diff=25658Directed Reading Program Fall 20232023-11-28T17:40:51Z<p>Jcobb2: Shortened david talks</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, December 6th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are closed.<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
{| class="wikitable"<br />
|+Fall 2023 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Analysis On Graphs<br />
|We will study analysis on graphs. More precisely, we will read the book ''Introduction to Analysis on Graphs'' by Alexander Grigor'yan. The purpose of the book is to provide an introduction to the subject of the discrete Laplace operator on locally finite graphs. Analysis on graphs is a subject studies classical calculus and differential equations on discrete objects such as graphs. It has connections with many other important areas in math and outside of math. <br />
|Students should be familiar with basic calculus (221, 222 and 234) and linear algebra. Analysis courses such as 521 and 522 or basic probability theory are helpful.<br />
|-<br />
|Analysis, Geometry, and Combinatorics<br />
|I am very flexible and happy to work with your backgrounds and interests. A few things I've thought about are:<br />
<br />
- Looking at Guth's book "Polynomial Method's in Combinatorics", hopefully culminating in understanding the proof of the finite field Kakeya conjecture. <br />
<br />
- Measure theory - we'll start with Stein & Shakarchi's book, depending on how that goes, we could move on to Frank Morgan's "Geometric Measure Theory: A Beginner’s Guide" for a bit of geometric measure theory.<br />
<br />
- Laszlo Lovasz's book "Combinatorial Problems and Exercises". The name is pretty self-explanatory - this books balances more towards problems and less towards theory, but won't require much background.<br />
<br />
- Spivak's book "Calculus on manifolds". This isn't your usual calculus book - it will introduce differential forms, which are very useful in geometry and analysis. <br />
|-<br />
|Fractal geometry<br />
|In recent years, a surprising connection between two seemingly unrelated branches of math has emerged. Fractal dimension is a notion of size for sets which, unlike how we normally think about dimension, is not necessarily an integer (e.g. the rough shape of a coastline, the branching of a bolt of lightning, or the chaotic movement of a stock's price have non-integer dimension). Kolmogorov complexity, which measures how much information a string contains, can be applied to characterize some types of fractal dimension. This connection has already yielded impressive new results about fractal sets. <br />
In this DRP, we will start by understanding notions of fractal dimension and the definition/properties of Kolmogorov complexity. Then, we'll bridge the gap between the two via "effective" dimension. Effective dimension gives rise to elegant characterizations of both Hausdorff and packing dimension via the recently proven point-to-set principle, which we will study. Finally, we'll see some applications of this alternative definition, which makes it one of the most powerful new tools in fractal geometry. <br />
|I would like students who have taken 521-522. But I'm flexible and happy to find something which you feel ready for.<br />
|-<br />
|Number theory and Partition Theory<br />
|We will investigate modular forms with a view towards algebraic combinatorics and number theory. In this project, we will first read about the interesting connections of modular forms and number theory/arithmetic geometry, with a focus on the theory of theta functions and elliptic curves. We will then transition to a more concrete application of modular forms via partition theory. In particular, we'll cover both analytic and combinatorial techniques, such as the circle method and enumerative combinatorics. We may also dive into more modern applications such as mock theta functions. Depending on participant interest this may turn into a research project based on prior work of the mentor on generalizing the Rogers-Ramanujan identities in partition theory. <br />
|Students should have completed a semester of algebra (541) and be familiar with proofs. Familiarity with complex analysis will be useful though not required. Coding knowledge with python would also be useful. <br />
|-<br />
|Measure Theory<br />
|Euclidean space may seem simple enough, but it contains many complicated subsets with highly counterintuitive properties. Throughout the semester, we'll consider a number of examples of such subsets, including the standard Cantor set, fat and thin Cantor sets, Vitali sets, "large" meager sets, purely unrectifiable sets, Kakeya sets, Nikodym sets, and many more. Readings will be provided and will come from a variety of sources, <br />
|Students should either have taken 521 or currently be enrolled in it. <br />
|-<br />
|Basics of D-modules<br />
|In this project, students will be introduced to D-modules, which allow us to think about ideas from calculus, such as derivatives and differential equations, in an algebraic context. The topics covered will include the Weyl algebra, the Jacobian conjecture, rings of differential operators, modules over the Weyl algebra, and differential equations. The text we will use is "A Primer of Algebraic D-modules" by S.C. Coutinho.<br />
|The prerequisite is math 541 or an equivalent: rings, ideals, homomorphisms, polynomial rings, and abstract vector spaces. A basic knowledge of modules is necessary, but this can be introduced at the beginning of the project.<br />
|-<br />
|Commutative Algebra<br />
|Ideals, Varieties, and Algorithms (Chapters 1-2) with a view toward algebraic geometry.Students are expected to give "mini-talks" on the board for the section we read that week. <br />
|Some knowledge of abstract algebra but not much else.<br />
|-<br />
|Computability Theory, or, Algebra<br />
|1, Computability Theory: we will focus on computability theory, complexity theory, and cryptography. There is a book called Computational Complexity: A Moder Approach, and we can pay more attention to Non-determinism and NP Completeness. <br />
<br />
2, Algebra: we will focus on Linear Representations of Finite Groups. It is also the name of a book which describes the correspondence, due to Frobenius, between linear representations and characters. The book says this is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics and have tried to give proofs as elementary as possible, using only the definition of a group and the rudiments of linear algebra.<br />
|Strong abilities of Analysis and Discrete Mathematics (including Algebra, etc)<br />
|-<br />
|Machine Learning<br />
| In this project, students will read/watch parts of the "Practical Deep Learning for Coders" course of fast.ai, a deep learning library that aims to make deep learning as accessible as possible, with the aim of training a basic machine learning model of their own design. In parallel, the students will also develop the skills for some software development practices, such as unit testing, documentation, and key bindings.<br />
|Calculus, Linear Algebra, and basic programming experience (preferably including Python) are required. I would also like the students to be mostly independent as designing their own machine learning model is a goal for this project (although this goal is not a hard requirement) and as I might be away for some weeks during the semester.<br />
|-<br />
|Dynamics (Analysis/Geometry)<br />
|Ergodic theory studies dynamical systems (we can think of this as a repeated action) and their statistical properties (i.e. time averages). For example, consider a circle and pick a point and an angle. Now our action will be repeatedly rotating the point by the chosen angle. Now if we do this action repeatedly for a long time, what will the resulting orbit of the point be? Will it miss part of the circle? Go everywhere? Go everywhere equally often? If we choose an irrational angle the last is true and we call the system ergodic. Ergodic theory is concerned with the study of these systems. While we won’t directly study them, ergodic theory has applications in many other fields -- including number theory, harmonic analysis, probability, and mathematical physics -- making it an incredibly exciting multi-disciplinary area to study. Our plan will be to first spend some time reviewing measure theory, then look at some examples and define ergodicity rigorously. After that we will spend some time studying the various ergodic theorems. If time allows we will extend our study to mixing and entropy.<br />
|The Real Analysis sequence (or equivalent) is required. Having seen some measure theory will be extremely helpful though we will spend the first week or two reviewing this topic. Any geometry/topology is useful but not at all required.<br />
|}<br />
<br />
== Presentation Schedule ==<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|+Room 1 (Van Vleck B329)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:45-4:00<br />
| bgcolor="#C6D46E" | Yikai Zhang & Beining Mu<br />
| bgcolor="#BCE2FE" | Computability<br />
|-<br />
| bgcolor="#E0E0E0" | 4:00-4:45<br />
| bgcolor="#C6D46E" | Aidin Simkin, Yifan Yang, Sena Witzeling<br />
| bgcolor="#BCE2FE" | Several Strange Cantor Sets<br />
|-<br />
| bgcolor="#E0E0E0" | 4:45-5:00<br />
| bgcolor="#C6D46E" | Yancheng Zhu<br />
| bgcolor="#BCE2FE" | FastAi in NLP<br />
|-<br />
| bgcolor="#E0E0E0" | 5:00-5:15<br />
| bgcolor="#C6D46E" | Shi Kaiwen<br />
| bgcolor="#BCE2FE" | Machine learning application in stock index prediction<br />
|-<br />
| bgcolor="#E0E0E0" | 5:15-5:30<br />
| bgcolor="#C6D46E" | Hannah Wang<br />
| bgcolor="#BCE2FE" | Trained model for predicting the insurance price<br />
|}<br />
</center><br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|+Room 2 (Van Vleck B333)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 4:00-4:30 <br />
| bgcolor="#C6D46E" | Aiden Styers, Rui Yu, Yizhou Qian & Anvith Aravati<br />
| bgcolor="#BCE2FE" | Laplace Operator on Graphs<br />
|-<br />
| bgcolor="#E0E0E0" | 4:30-5:00<br />
| bgcolor="#C6D46E" | Benjamin Braiman & Ruoyu Men<br />
| bgcolor="#BCE2FE" | Ergodic Theory<br />
|-<br />
| bgcolor="#E0E0E0" | 5:00-5:15<br />
| bgcolor="#C6D46E" | David Jiang<br />
| bgcolor="#BCE2FE" | Ramanujan Partition Identities<br />
|}<br />
</center></div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Fall_2023&diff=25657Directed Reading Program Fall 20232023-11-28T16:18:54Z<p>Jcobb2: /* Presentation Schedule */</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, December 6th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are closed.<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
{| class="wikitable"<br />
|+Fall 2023 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Analysis On Graphs<br />
|We will study analysis on graphs. More precisely, we will read the book ''Introduction to Analysis on Graphs'' by Alexander Grigor'yan. The purpose of the book is to provide an introduction to the subject of the discrete Laplace operator on locally finite graphs. Analysis on graphs is a subject studies classical calculus and differential equations on discrete objects such as graphs. It has connections with many other important areas in math and outside of math. <br />
|Students should be familiar with basic calculus (221, 222 and 234) and linear algebra. Analysis courses such as 521 and 522 or basic probability theory are helpful.<br />
|-<br />
|Analysis, Geometry, and Combinatorics<br />
|I am very flexible and happy to work with your backgrounds and interests. A few things I've thought about are:<br />
<br />
- Looking at Guth's book "Polynomial Method's in Combinatorics", hopefully culminating in understanding the proof of the finite field Kakeya conjecture. <br />
<br />
- Measure theory - we'll start with Stein & Shakarchi's book, depending on how that goes, we could move on to Frank Morgan's "Geometric Measure Theory: A Beginner’s Guide" for a bit of geometric measure theory.<br />
<br />
- Laszlo Lovasz's book "Combinatorial Problems and Exercises". The name is pretty self-explanatory - this books balances more towards problems and less towards theory, but won't require much background.<br />
<br />
- Spivak's book "Calculus on manifolds". This isn't your usual calculus book - it will introduce differential forms, which are very useful in geometry and analysis. <br />
|-<br />
|Fractal geometry<br />
|In recent years, a surprising connection between two seemingly unrelated branches of math has emerged. Fractal dimension is a notion of size for sets which, unlike how we normally think about dimension, is not necessarily an integer (e.g. the rough shape of a coastline, the branching of a bolt of lightning, or the chaotic movement of a stock's price have non-integer dimension). Kolmogorov complexity, which measures how much information a string contains, can be applied to characterize some types of fractal dimension. This connection has already yielded impressive new results about fractal sets. <br />
In this DRP, we will start by understanding notions of fractal dimension and the definition/properties of Kolmogorov complexity. Then, we'll bridge the gap between the two via "effective" dimension. Effective dimension gives rise to elegant characterizations of both Hausdorff and packing dimension via the recently proven point-to-set principle, which we will study. Finally, we'll see some applications of this alternative definition, which makes it one of the most powerful new tools in fractal geometry. <br />
|I would like students who have taken 521-522. But I'm flexible and happy to find something which you feel ready for.<br />
|-<br />
|Number theory and Partition Theory<br />
|We will investigate modular forms with a view towards algebraic combinatorics and number theory. In this project, we will first read about the interesting connections of modular forms and number theory/arithmetic geometry, with a focus on the theory of theta functions and elliptic curves. We will then transition to a more concrete application of modular forms via partition theory. In particular, we'll cover both analytic and combinatorial techniques, such as the circle method and enumerative combinatorics. We may also dive into more modern applications such as mock theta functions. Depending on participant interest this may turn into a research project based on prior work of the mentor on generalizing the Rogers-Ramanujan identities in partition theory. <br />
|Students should have completed a semester of algebra (541) and be familiar with proofs. Familiarity with complex analysis will be useful though not required. Coding knowledge with python would also be useful. <br />
|-<br />
|Measure Theory<br />
|Euclidean space may seem simple enough, but it contains many complicated subsets with highly counterintuitive properties. Throughout the semester, we'll consider a number of examples of such subsets, including the standard Cantor set, fat and thin Cantor sets, Vitali sets, "large" meager sets, purely unrectifiable sets, Kakeya sets, Nikodym sets, and many more. Readings will be provided and will come from a variety of sources, <br />
|Students should either have taken 521 or currently be enrolled in it. <br />
|-<br />
|Basics of D-modules<br />
|In this project, students will be introduced to D-modules, which allow us to think about ideas from calculus, such as derivatives and differential equations, in an algebraic context. The topics covered will include the Weyl algebra, the Jacobian conjecture, rings of differential operators, modules over the Weyl algebra, and differential equations. The text we will use is "A Primer of Algebraic D-modules" by S.C. Coutinho.<br />
|The prerequisite is math 541 or an equivalent: rings, ideals, homomorphisms, polynomial rings, and abstract vector spaces. A basic knowledge of modules is necessary, but this can be introduced at the beginning of the project.<br />
|-<br />
|Commutative Algebra<br />
|Ideals, Varieties, and Algorithms (Chapters 1-2) with a view toward algebraic geometry.Students are expected to give "mini-talks" on the board for the section we read that week. <br />
|Some knowledge of abstract algebra but not much else.<br />
|-<br />
|Computability Theory, or, Algebra<br />
|1, Computability Theory: we will focus on computability theory, complexity theory, and cryptography. There is a book called Computational Complexity: A Moder Approach, and we can pay more attention to Non-determinism and NP Completeness. <br />
<br />
2, Algebra: we will focus on Linear Representations of Finite Groups. It is also the name of a book which describes the correspondence, due to Frobenius, between linear representations and characters. The book says this is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics and have tried to give proofs as elementary as possible, using only the definition of a group and the rudiments of linear algebra.<br />
|Strong abilities of Analysis and Discrete Mathematics (including Algebra, etc)<br />
|-<br />
|Machine Learning<br />
| In this project, students will read/watch parts of the "Practical Deep Learning for Coders" course of fast.ai, a deep learning library that aims to make deep learning as accessible as possible, with the aim of training a basic machine learning model of their own design. In parallel, the students will also develop the skills for some software development practices, such as unit testing, documentation, and key bindings.<br />
|Calculus, Linear Algebra, and basic programming experience (preferably including Python) are required. I would also like the students to be mostly independent as designing their own machine learning model is a goal for this project (although this goal is not a hard requirement) and as I might be away for some weeks during the semester.<br />
|-<br />
|Dynamics (Analysis/Geometry)<br />
|Ergodic theory studies dynamical systems (we can think of this as a repeated action) and their statistical properties (i.e. time averages). For example, consider a circle and pick a point and an angle. Now our action will be repeatedly rotating the point by the chosen angle. Now if we do this action repeatedly for a long time, what will the resulting orbit of the point be? Will it miss part of the circle? Go everywhere? Go everywhere equally often? If we choose an irrational angle the last is true and we call the system ergodic. Ergodic theory is concerned with the study of these systems. While we won’t directly study them, ergodic theory has applications in many other fields -- including number theory, harmonic analysis, probability, and mathematical physics -- making it an incredibly exciting multi-disciplinary area to study. Our plan will be to first spend some time reviewing measure theory, then look at some examples and define ergodicity rigorously. After that we will spend some time studying the various ergodic theorems. If time allows we will extend our study to mixing and entropy.<br />
|The Real Analysis sequence (or equivalent) is required. Having seen some measure theory will be extremely helpful though we will spend the first week or two reviewing this topic. Any geometry/topology is useful but not at all required.<br />
|}<br />
<br />
== Presentation Schedule ==<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|+Room 1 (Van Vleck B329)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:45-4:00<br />
| bgcolor="#C6D46E" | Yikai Zhang & Beining Mu<br />
| bgcolor="#BCE2FE" | Computability<br />
|-<br />
| bgcolor="#E0E0E0" | 4:00-4:45<br />
| bgcolor="#C6D46E" | Aidin Simkin, Yifan Yang, Sena Witzeling<br />
| bgcolor="#BCE2FE" | Several Strange Cantor Sets<br />
|-<br />
| bgcolor="#E0E0E0" | 4:45-5:00<br />
| bgcolor="#C6D46E" | Yancheng Zhu<br />
| bgcolor="#BCE2FE" | FastAi in NLP<br />
|-<br />
| bgcolor="#E0E0E0" | 5:00-5:15<br />
| bgcolor="#C6D46E" | Shi Kaiwen<br />
| bgcolor="#BCE2FE" | Machine learning application in stock index prediction<br />
|-<br />
| bgcolor="#E0E0E0" | 5:15-5:30<br />
| bgcolor="#C6D46E" | Hannah Wang<br />
| bgcolor="#BCE2FE" | Trained model for predicting the insurance price<br />
|}<br />
</center><br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|+Room 2 (Van Vleck B333)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 4:00-4:30 <br />
| bgcolor="#C6D46E" | Aiden Styers, Rui Yu, Yizhou Qian & Anvith Aravati<br />
| bgcolor="#BCE2FE" | Laplace Operator on Graphs<br />
|-<br />
| bgcolor="#E0E0E0" | 4:30-5:00<br />
| bgcolor="#C6D46E" | Benjamin Braiman & Ruoyu Men<br />
| bgcolor="#BCE2FE" | Ergodic Theory<br />
|-<br />
| bgcolor="#E0E0E0" | 5:00-5:30<br />
| bgcolor="#C6D46E" | David Jiang<br />
| bgcolor="#BCE2FE" | Ramanujan Partition Identities<br />
|}<br />
</center></div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Fall_2023&diff=25655Directed Reading Program Fall 20232023-11-27T23:31:25Z<p>Jcobb2: /* Presentation Schedule */</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, December 6th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are closed.<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
{| class="wikitable"<br />
|+Fall 2023 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Analysis On Graphs<br />
|We will study analysis on graphs. More precisely, we will read the book ''Introduction to Analysis on Graphs'' by Alexander Grigor'yan. The purpose of the book is to provide an introduction to the subject of the discrete Laplace operator on locally finite graphs. Analysis on graphs is a subject studies classical calculus and differential equations on discrete objects such as graphs. It has connections with many other important areas in math and outside of math. <br />
|Students should be familiar with basic calculus (221, 222 and 234) and linear algebra. Analysis courses such as 521 and 522 or basic probability theory are helpful.<br />
|-<br />
|Analysis, Geometry, and Combinatorics<br />
|I am very flexible and happy to work with your backgrounds and interests. A few things I've thought about are:<br />
<br />
- Looking at Guth's book "Polynomial Method's in Combinatorics", hopefully culminating in understanding the proof of the finite field Kakeya conjecture. <br />
<br />
- Measure theory - we'll start with Stein & Shakarchi's book, depending on how that goes, we could move on to Frank Morgan's "Geometric Measure Theory: A Beginner’s Guide" for a bit of geometric measure theory.<br />
<br />
- Laszlo Lovasz's book "Combinatorial Problems and Exercises". The name is pretty self-explanatory - this books balances more towards problems and less towards theory, but won't require much background.<br />
<br />
- Spivak's book "Calculus on manifolds". This isn't your usual calculus book - it will introduce differential forms, which are very useful in geometry and analysis. <br />
|-<br />
|Fractal geometry<br />
|In recent years, a surprising connection between two seemingly unrelated branches of math has emerged. Fractal dimension is a notion of size for sets which, unlike how we normally think about dimension, is not necessarily an integer (e.g. the rough shape of a coastline, the branching of a bolt of lightning, or the chaotic movement of a stock's price have non-integer dimension). Kolmogorov complexity, which measures how much information a string contains, can be applied to characterize some types of fractal dimension. This connection has already yielded impressive new results about fractal sets. <br />
In this DRP, we will start by understanding notions of fractal dimension and the definition/properties of Kolmogorov complexity. Then, we'll bridge the gap between the two via "effective" dimension. Effective dimension gives rise to elegant characterizations of both Hausdorff and packing dimension via the recently proven point-to-set principle, which we will study. Finally, we'll see some applications of this alternative definition, which makes it one of the most powerful new tools in fractal geometry. <br />
|I would like students who have taken 521-522. But I'm flexible and happy to find something which you feel ready for.<br />
|-<br />
|Number theory and Partition Theory<br />
|We will investigate modular forms with a view towards algebraic combinatorics and number theory. In this project, we will first read about the interesting connections of modular forms and number theory/arithmetic geometry, with a focus on the theory of theta functions and elliptic curves. We will then transition to a more concrete application of modular forms via partition theory. In particular, we'll cover both analytic and combinatorial techniques, such as the circle method and enumerative combinatorics. We may also dive into more modern applications such as mock theta functions. Depending on participant interest this may turn into a research project based on prior work of the mentor on generalizing the Rogers-Ramanujan identities in partition theory. <br />
|Students should have completed a semester of algebra (541) and be familiar with proofs. Familiarity with complex analysis will be useful though not required. Coding knowledge with python would also be useful. <br />
|-<br />
|Measure Theory<br />
|Euclidean space may seem simple enough, but it contains many complicated subsets with highly counterintuitive properties. Throughout the semester, we'll consider a number of examples of such subsets, including the standard Cantor set, fat and thin Cantor sets, Vitali sets, "large" meager sets, purely unrectifiable sets, Kakeya sets, Nikodym sets, and many more. Readings will be provided and will come from a variety of sources, <br />
|Students should either have taken 521 or currently be enrolled in it. <br />
|-<br />
|Basics of D-modules<br />
|In this project, students will be introduced to D-modules, which allow us to think about ideas from calculus, such as derivatives and differential equations, in an algebraic context. The topics covered will include the Weyl algebra, the Jacobian conjecture, rings of differential operators, modules over the Weyl algebra, and differential equations. The text we will use is "A Primer of Algebraic D-modules" by S.C. Coutinho.<br />
|The prerequisite is math 541 or an equivalent: rings, ideals, homomorphisms, polynomial rings, and abstract vector spaces. A basic knowledge of modules is necessary, but this can be introduced at the beginning of the project.<br />
|-<br />
|Commutative Algebra<br />
|Ideals, Varieties, and Algorithms (Chapters 1-2) with a view toward algebraic geometry.Students are expected to give "mini-talks" on the board for the section we read that week. <br />
|Some knowledge of abstract algebra but not much else.<br />
|-<br />
|Computability Theory, or, Algebra<br />
|1, Computability Theory: we will focus on computability theory, complexity theory, and cryptography. There is a book called Computational Complexity: A Moder Approach, and we can pay more attention to Non-determinism and NP Completeness. <br />
<br />
2, Algebra: we will focus on Linear Representations of Finite Groups. It is also the name of a book which describes the correspondence, due to Frobenius, between linear representations and characters. The book says this is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics and have tried to give proofs as elementary as possible, using only the definition of a group and the rudiments of linear algebra.<br />
|Strong abilities of Analysis and Discrete Mathematics (including Algebra, etc)<br />
|-<br />
|Machine Learning<br />
| In this project, students will read/watch parts of the "Practical Deep Learning for Coders" course of fast.ai, a deep learning library that aims to make deep learning as accessible as possible, with the aim of training a basic machine learning model of their own design. In parallel, the students will also develop the skills for some software development practices, such as unit testing, documentation, and key bindings.<br />
|Calculus, Linear Algebra, and basic programming experience (preferably including Python) are required. I would also like the students to be mostly independent as designing their own machine learning model is a goal for this project (although this goal is not a hard requirement) and as I might be away for some weeks during the semester.<br />
|-<br />
|Dynamics (Analysis/Geometry)<br />
|Ergodic theory studies dynamical systems (we can think of this as a repeated action) and their statistical properties (i.e. time averages). For example, consider a circle and pick a point and an angle. Now our action will be repeatedly rotating the point by the chosen angle. Now if we do this action repeatedly for a long time, what will the resulting orbit of the point be? Will it miss part of the circle? Go everywhere? Go everywhere equally often? If we choose an irrational angle the last is true and we call the system ergodic. Ergodic theory is concerned with the study of these systems. While we won’t directly study them, ergodic theory has applications in many other fields -- including number theory, harmonic analysis, probability, and mathematical physics -- making it an incredibly exciting multi-disciplinary area to study. Our plan will be to first spend some time reviewing measure theory, then look at some examples and define ergodicity rigorously. After that we will spend some time studying the various ergodic theorems. If time allows we will extend our study to mixing and entropy.<br />
|The Real Analysis sequence (or equivalent) is required. Having seen some measure theory will be extremely helpful though we will spend the first week or two reviewing this topic. Any geometry/topology is useful but not at all required.<br />
|}<br />
<br />
== Presentation Schedule ==<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|+Room 1<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:45-4:00<br />
| bgcolor="#C6D46E" | Yikai Zhang & Beining Mu<br />
| bgcolor="#BCE2FE" | Computability<br />
|-<br />
| bgcolor="#E0E0E0" | 4:00-4:45<br />
| bgcolor="#C6D46E" | Aidin Simkin, Yifan Yang, Sena Witzeling<br />
| bgcolor="#BCE2FE" | Several Strange Cantor Sets<br />
|-<br />
| bgcolor="#E0E0E0" | 4:45-5:00<br />
| bgcolor="#C6D46E" | Yancheng Zhu<br />
| bgcolor="#BCE2FE" | FastAi in NLP<br />
|-<br />
| bgcolor="#E0E0E0" | 5:00-5:15<br />
| bgcolor="#C6D46E" | Shi Kaiwen<br />
| bgcolor="#BCE2FE" | Machine learning application in stock index prediction<br />
|-<br />
| bgcolor="#E0E0E0" | 5:15-5:30<br />
| bgcolor="#C6D46E" | Hannah Wang<br />
| bgcolor="#BCE2FE" | Trained model for predicting the insurance price<br />
|}<br />
</center><br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|+Room 2<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 4:00-4:30 <br />
| bgcolor="#C6D46E" | Aiden Styers, Rui Yu, Yizhou Qian & Anvith Aravati<br />
| bgcolor="#BCE2FE" | Laplace Operator on Graphs<br />
|-<br />
| bgcolor="#E0E0E0" | 4:30-5:00<br />
| bgcolor="#C6D46E" | Benjamin Braiman & Ruoyu Men<br />
| bgcolor="#BCE2FE" | Ergodic Theory<br />
|-<br />
| bgcolor="#E0E0E0" | 5:00-5:30<br />
| bgcolor="#C6D46E" | David Jiang<br />
| bgcolor="#BCE2FE" | Ramanujan Partition Identities<br />
|}<br />
</center></div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Fall_2023&diff=25647Directed Reading Program Fall 20232023-11-27T19:55:51Z<p>Jcobb2: Add presentation schedule.</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, December 6th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are closed.<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
{| class="wikitable"<br />
|+Fall 2023 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Analysis On Graphs<br />
|We will study analysis on graphs. More precisely, we will read the book ''Introduction to Analysis on Graphs'' by Alexander Grigor'yan. The purpose of the book is to provide an introduction to the subject of the discrete Laplace operator on locally finite graphs. Analysis on graphs is a subject studies classical calculus and differential equations on discrete objects such as graphs. It has connections with many other important areas in math and outside of math. <br />
|Students should be familiar with basic calculus (221, 222 and 234) and linear algebra. Analysis courses such as 521 and 522 or basic probability theory are helpful.<br />
|-<br />
|Analysis, Geometry, and Combinatorics<br />
|I am very flexible and happy to work with your backgrounds and interests. A few things I've thought about are:<br />
<br />
- Looking at Guth's book "Polynomial Method's in Combinatorics", hopefully culminating in understanding the proof of the finite field Kakeya conjecture. <br />
<br />
- Measure theory - we'll start with Stein & Shakarchi's book, depending on how that goes, we could move on to Frank Morgan's "Geometric Measure Theory: A Beginner’s Guide" for a bit of geometric measure theory.<br />
<br />
- Laszlo Lovasz's book "Combinatorial Problems and Exercises". The name is pretty self-explanatory - this books balances more towards problems and less towards theory, but won't require much background.<br />
<br />
- Spivak's book "Calculus on manifolds". This isn't your usual calculus book - it will introduce differential forms, which are very useful in geometry and analysis. <br />
|-<br />
|Fractal geometry<br />
|In recent years, a surprising connection between two seemingly unrelated branches of math has emerged. Fractal dimension is a notion of size for sets which, unlike how we normally think about dimension, is not necessarily an integer (e.g. the rough shape of a coastline, the branching of a bolt of lightning, or the chaotic movement of a stock's price have non-integer dimension). Kolmogorov complexity, which measures how much information a string contains, can be applied to characterize some types of fractal dimension. This connection has already yielded impressive new results about fractal sets. <br />
In this DRP, we will start by understanding notions of fractal dimension and the definition/properties of Kolmogorov complexity. Then, we'll bridge the gap between the two via "effective" dimension. Effective dimension gives rise to elegant characterizations of both Hausdorff and packing dimension via the recently proven point-to-set principle, which we will study. Finally, we'll see some applications of this alternative definition, which makes it one of the most powerful new tools in fractal geometry. <br />
|I would like students who have taken 521-522. But I'm flexible and happy to find something which you feel ready for.<br />
|-<br />
|Number theory and Partition Theory<br />
|We will investigate modular forms with a view towards algebraic combinatorics and number theory. In this project, we will first read about the interesting connections of modular forms and number theory/arithmetic geometry, with a focus on the theory of theta functions and elliptic curves. We will then transition to a more concrete application of modular forms via partition theory. In particular, we'll cover both analytic and combinatorial techniques, such as the circle method and enumerative combinatorics. We may also dive into more modern applications such as mock theta functions. Depending on participant interest this may turn into a research project based on prior work of the mentor on generalizing the Rogers-Ramanujan identities in partition theory. <br />
|Students should have completed a semester of algebra (541) and be familiar with proofs. Familiarity with complex analysis will be useful though not required. Coding knowledge with python would also be useful. <br />
|-<br />
|Measure Theory<br />
|Euclidean space may seem simple enough, but it contains many complicated subsets with highly counterintuitive properties. Throughout the semester, we'll consider a number of examples of such subsets, including the standard Cantor set, fat and thin Cantor sets, Vitali sets, "large" meager sets, purely unrectifiable sets, Kakeya sets, Nikodym sets, and many more. Readings will be provided and will come from a variety of sources, <br />
|Students should either have taken 521 or currently be enrolled in it. <br />
|-<br />
|Basics of D-modules<br />
|In this project, students will be introduced to D-modules, which allow us to think about ideas from calculus, such as derivatives and differential equations, in an algebraic context. The topics covered will include the Weyl algebra, the Jacobian conjecture, rings of differential operators, modules over the Weyl algebra, and differential equations. The text we will use is "A Primer of Algebraic D-modules" by S.C. Coutinho.<br />
|The prerequisite is math 541 or an equivalent: rings, ideals, homomorphisms, polynomial rings, and abstract vector spaces. A basic knowledge of modules is necessary, but this can be introduced at the beginning of the project.<br />
|-<br />
|Commutative Algebra<br />
|Ideals, Varieties, and Algorithms (Chapters 1-2) with a view toward algebraic geometry.Students are expected to give "mini-talks" on the board for the section we read that week. <br />
|Some knowledge of abstract algebra but not much else.<br />
|-<br />
|Computability Theory, or, Algebra<br />
|1, Computability Theory: we will focus on computability theory, complexity theory, and cryptography. There is a book called Computational Complexity: A Moder Approach, and we can pay more attention to Non-determinism and NP Completeness. <br />
<br />
2, Algebra: we will focus on Linear Representations of Finite Groups. It is also the name of a book which describes the correspondence, due to Frobenius, between linear representations and characters. The book says this is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics and have tried to give proofs as elementary as possible, using only the definition of a group and the rudiments of linear algebra.<br />
|Strong abilities of Analysis and Discrete Mathematics (including Algebra, etc)<br />
|-<br />
|Machine Learning<br />
| In this project, students will read/watch parts of the "Practical Deep Learning for Coders" course of fast.ai, a deep learning library that aims to make deep learning as accessible as possible, with the aim of training a basic machine learning model of their own design. In parallel, the students will also develop the skills for some software development practices, such as unit testing, documentation, and key bindings.<br />
|Calculus, Linear Algebra, and basic programming experience (preferably including Python) are required. I would also like the students to be mostly independent as designing their own machine learning model is a goal for this project (although this goal is not a hard requirement) and as I might be away for some weeks during the semester.<br />
|-<br />
|Dynamics (Analysis/Geometry)<br />
|Ergodic theory studies dynamical systems (we can think of this as a repeated action) and their statistical properties (i.e. time averages). For example, consider a circle and pick a point and an angle. Now our action will be repeatedly rotating the point by the chosen angle. Now if we do this action repeatedly for a long time, what will the resulting orbit of the point be? Will it miss part of the circle? Go everywhere? Go everywhere equally often? If we choose an irrational angle the last is true and we call the system ergodic. Ergodic theory is concerned with the study of these systems. While we won’t directly study them, ergodic theory has applications in many other fields -- including number theory, harmonic analysis, probability, and mathematical physics -- making it an incredibly exciting multi-disciplinary area to study. Our plan will be to first spend some time reviewing measure theory, then look at some examples and define ergodicity rigorously. After that we will spend some time studying the various ergodic theorems. If time allows we will extend our study to mixing and entropy.<br />
|The Real Analysis sequence (or equivalent) is required. Having seen some measure theory will be extremely helpful though we will spend the first week or two reviewing this topic. Any geometry/topology is useful but not at all required.<br />
|}<br />
<br />
== Presentation Schedule ==<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|+Room 1<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:45-4:00<br />
| bgcolor="#C6D46E" | Yikai Zhang & Beining Mu<br />
| bgcolor="#BCE2FE" | Computability<br />
|-<br />
| bgcolor="#E0E0E0" | 4:00-4:45<br />
| bgcolor="#C6D46E" | Aidin Simkin, Yifan Yang, Sena Witzeling<br />
| bgcolor="#BCE2FE" | Several Strange Cantor Sets<br />
|-<br />
| bgcolor="#E0E0E0" | 4:45-5:00<br />
| bgcolor="#C6D46E" | Yancheng Zhu<br />
| bgcolor="#BCE2FE" | FastAi in NLP<br />
|-<br />
| bgcolor="#E0E0E0" | 5:00-5:15<br />
| bgcolor="#C6D46E" | Shi Kaiwen<br />
| bgcolor="#BCE2FE" | Machine learning application in stock index prediction<br />
|-<br />
| bgcolor="#E0E0E0" | 5:15-5:30<br />
| bgcolor="#C6D46E" | Hannah Wang<br />
| bgcolor="#BCE2FE" | Trained model for predicting the insurance price<br />
|}<br />
</center><br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|+Room 2<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:30-4:30 <br />
| bgcolor="#C6D46E" | Aiden Styers, Rui Yu, Yizhou Qian & Anvith Aravati<br />
| bgcolor="#BCE2FE" | Laplace Operator on Graphs<br />
|-<br />
| bgcolor="#E0E0E0" | 4:30-5:00<br />
| bgcolor="#C6D46E" | Benjamin Braiman & Ruoyu Men<br />
| bgcolor="#BCE2FE" | Ergodic Theory<br />
|-<br />
| bgcolor="#E0E0E0" | 5:00-5:30<br />
| bgcolor="#C6D46E" | David Jiang<br />
| bgcolor="#BCE2FE" | Ramanujan Partition Identities<br />
|}<br />
</center></div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25602Graduate Algebraic Geometry Seminar Fall 20232023-11-17T17:50:10Z<p>Jcobb2: /* Talks */</p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' Van Vleck B119<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/fNgXzpn7QAJM4Ybo9 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="200" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="200" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
| bgcolor="#BCD2EE" width="400" align="center" |'''Abstract'''<br />
|-<br />
| bgcolor="#E0E0E0" |September 13<br />
| bgcolor="#C6D46E" | Peter Wei<br />
| bgcolor="#BCE2FE" | Introduction to the Cartier Isomorphism (Pretalk)<br />
| bgcolor="#BCE2FE" | This is a preparatory talk for Josh Mundinger's talk on Friday. We discuss the Cartier isomorphism. <br />
|-<br />
| bgcolor="#E0E0E0" |September 20<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |September 27<br />
| bgcolor="#C6D46E" |Yifan Wei<br />
| bgcolor="#BCE2FE" |p-torsions in the p-adic land and de Rham cohomology<br />
| bgcolor="#BCE2FE" | Following Tate, we will try to visualize an elliptic curve over Cp, specifically, the p-adic disk near identity. Logarithm in the p-adic land provides a nice linearization to the problem, and we'll explore what this all means. If time permits, I'll sketch the proof of Hodge-Tate decomposition. (You know something like this is coming.)<br />
|-<br />
| bgcolor="#E0E0E0" |October 4<br />
| bgcolor="#C6D46E" |Owen Goff<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 11<br />
| bgcolor="#C6D46E" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 18<br />
| bgcolor="#C6D46E" |Alex Hof<br />
| bgcolor="#BCE2FE" |Why Does Normalization Resolve Singularities in Codimension 1?<br />
| bgcolor="#BCE2FE" |We review the definition of the normalization of an algebraic variety, discuss the geometric intuition for it, and explain why normalizing removes codimension-1 singularities. This talk is intended to be accessible to people taking first-semester algebraic geometry.<br />
|-<br />
| bgcolor="#E0E0E0" | October 25<br />
| bgcolor="#C6D46E" |Jack Messina<br />
| bgcolor="#BCE2FE" |Variations of Hodge Structure and Hodge Modules<br />
| bgcolor="#BCE2FE" | This talk aims to introduce Hodge modules. We will start with the classical variation of Hodge structure, and then cover some background on perverse sheaves and D-modules. From here, we can introduce pure Hodge modules. We end by mentioning mixed Hodge modules and the Saito vanishing theorem.<br />
|-<br />
| bgcolor="#E0E0E0" | November 1<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | November 8<br />
| bgcolor="#C6D46E" |John Cobb<br />
| bgcolor="#BCE2FE" |Likelihood Geometry<br />
| bgcolor="#BCE2FE" |Maximum likelihood estimation (MLE) is a fundamental task in statistics. June Huh and Bernd Sturmfels wrote a long paper that explores how characteristics of the MLE problem for algebraic statistical models are reflected in the geometry of the likelihood correspondence, a variety that ties together observed data and their maximum likelihood estimators. I’ll define these objects, frame some questions (with partial answers) about them, and give some cool facts coming from algebraic statistics. This will be adapted from a much shorter talk, so there will be plenty of time for tangents and questions!<br />
|-<br />
| bgcolor="#E0E0E0" | November 15<br />
| bgcolor="#C6D46E" |Peter Wei<br />
| bgcolor="#BCE2FE" |Pretalk for Purnaprajna Bangere's talk<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 22<br />
| bgcolor="#C6D46E" |Thanksgiving Break<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 29<br />
| bgcolor="#C6D46E" |Yanbo Chen<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | December 9<br />
| bgcolor="#C6D46E" | Kevin Dao<br />
| bgcolor="#BCE2FE" |Introduction to D-Modules<br />
| bgcolor="#BCE2FE" |On the basics of the theory of D-Modules and how it gets used.<br />
|-<br />
| bgcolor="#E0E0E0" | December 13<br />
| bgcolor="#C6D46E" | Maya Banks<br />
| bgcolor="#BCE2FE" | <br />
| bgcolor="#BCE2FE" |<br />
|}<br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023] <br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022] [https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022] <br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25589Graduate Algebraic Geometry Seminar Fall 20232023-11-14T17:04:33Z<p>Jcobb2: /* Talks */</p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' Van Vleck B119<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/fNgXzpn7QAJM4Ybo9 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="200" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="200" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
| bgcolor="#BCD2EE" width="400" align="center" |'''Abstract'''<br />
|-<br />
| bgcolor="#E0E0E0" |September 13<br />
| bgcolor="#C6D46E" | Peter Wei<br />
| bgcolor="#BCE2FE" | Introduction to the Cartier Isomorphism (Pretalk)<br />
| bgcolor="#BCE2FE" | This is a preparatory talk for Josh Mundinger's talk on Friday. We discuss the Cartier isomorphism. <br />
|-<br />
| bgcolor="#E0E0E0" |September 20<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |September 27<br />
| bgcolor="#C6D46E" |Yifan Wei<br />
| bgcolor="#BCE2FE" |p-torsions in the p-adic land and de Rham cohomology<br />
| bgcolor="#BCE2FE" | Following Tate, we will try to visualize an elliptic curve over Cp, specifically, the p-adic disk near identity. Logarithm in the p-adic land provides a nice linearization to the problem, and we'll explore what this all means. If time permits, I'll sketch the proof of Hodge-Tate decomposition. (You know something like this is coming.)<br />
|-<br />
| bgcolor="#E0E0E0" |October 4<br />
| bgcolor="#C6D46E" |Owen Goff<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 11<br />
| bgcolor="#C6D46E" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 18<br />
| bgcolor="#C6D46E" |Alex Hof<br />
| bgcolor="#BCE2FE" |Why Does Normalization Resolve Singularities in Codimension 1?<br />
| bgcolor="#BCE2FE" |We review the definition of the normalization of an algebraic variety, discuss the geometric intuition for it, and explain why normalizing removes codimension-1 singularities. This talk is intended to be accessible to people taking first-semester algebraic geometry.<br />
|-<br />
| bgcolor="#E0E0E0" | October 25<br />
| bgcolor="#C6D46E" |Jack Messina<br />
| bgcolor="#BCE2FE" |Variations of Hodge Structure and Hodge Modules<br />
| bgcolor="#BCE2FE" | This talk aims to introduce Hodge modules. We will start with the classical variation of Hodge structure, and then cover some background on perverse sheaves and D-modules. From here, we can introduce pure Hodge modules. We end by mentioning mixed Hodge modules and the Saito vanishing theorem.<br />
|-<br />
| bgcolor="#E0E0E0" | November 1<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | November 8<br />
| bgcolor="#C6D46E" |John Cobb<br />
| bgcolor="#BCE2FE" |Likelihood Geometry<br />
| bgcolor="#BCE2FE" |Maximum likelihood estimation (MLE) is a fundamental task in statistics. June Huh and Bernd Sturmfels wrote a long paper that explores how characteristics of the MLE problem for algebraic statistical models are reflected in the geometry of the likelihood correspondence, a variety that ties together observed data and their maximum likelihood estimators. I’ll define these objects, frame some questions (with partial answers) about them, and give some cool facts coming from algebraic statistics. This will be adapted from a much shorter talk, so there will be plenty of time for tangents and questions!<br />
|-<br />
| bgcolor="#E0E0E0" | November 15<br />
| bgcolor="#C6D46E" |Peter Wei<br />
| bgcolor="#BCE2FE" |Pretalk for Purnaprajna Bangere's talk<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 22<br />
| bgcolor="#C6D46E" |Alex Mine<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 29<br />
| bgcolor="#C6D46E" |Yanbo Chen<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | December 9<br />
| bgcolor="#C6D46E" | Kevin Dao<br />
| bgcolor="#BCE2FE" |Introduction to D-Modules<br />
| bgcolor="#BCE2FE" |On the basics of the theory of D-Modules and how it gets used.<br />
|-<br />
| bgcolor="#E0E0E0" | December 13<br />
| bgcolor="#C6D46E" | Maya Banks<br />
| bgcolor="#BCE2FE" | <br />
| bgcolor="#BCE2FE" |<br />
|}<br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023] <br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022] [https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022] <br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25484Graduate Algebraic Geometry Seminar Fall 20232023-10-24T13:37:09Z<p>Jcobb2: </p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' Van Vleck B119<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/fNgXzpn7QAJM4Ybo9 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="200" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="200" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
| bgcolor="#BCD2EE" width="400" align="center" |'''Abstract'''<br />
|-<br />
| bgcolor="#E0E0E0" |September 13<br />
| bgcolor="#C6D46E" | Peter Wei<br />
| bgcolor="#BCE2FE" | Introduction to the Cartier Isomorphism (Pretalk)<br />
| bgcolor="#BCE2FE" | This is a preparatory talk for Josh Mundinger's talk on Friday. We discuss the Cartier isomorphism. <br />
|-<br />
| bgcolor="#E0E0E0" |September 20<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |September 27<br />
| bgcolor="#C6D46E" |Yifan Wei<br />
| bgcolor="#BCE2FE" |p-torsions in the p-adic land and de Rham cohomology<br />
| bgcolor="#BCE2FE" | Following Tate, we will try to visualize an elliptic curve over Cp, specifically, the p-adic disk near identity. Logarithm in the p-adic land provides a nice linearization to the problem, and we'll explore what this all means. If time permits, I'll sketch the proof of Hodge-Tate decomposition. (You know something like this is coming.)<br />
|-<br />
| bgcolor="#E0E0E0" |October 4<br />
| bgcolor="#C6D46E" |Owen Goff<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 11<br />
| bgcolor="#C6D46E" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 18<br />
| bgcolor="#C6D46E" |Alex Hof<br />
| bgcolor="#BCE2FE" |Why Does Normalization Resolve Singularities in Codimension 1?<br />
| bgcolor="#BCE2FE" |We review the definition of the normalization of an algebraic variety, discuss the geometric intuition for it, and explain why normalizing removes codimension-1 singularities. This talk is intended to be accessible to people taking first-semester algebraic geometry.<br />
|-<br />
| bgcolor="#E0E0E0" | October 25<br />
| bgcolor="#C6D46E" |Jack Messina<br />
| bgcolor="#BCE2FE" |Variations of Hodge Structure and Hodge Modules<br />
| bgcolor="#BCE2FE" | This talk aims to introduce Hodge modules. We will start with the classical variation of Hodge structure, and then cover some background on perverse sheaves and D-modules. From here, we can introduce pure Hodge modules. We end by mentioning mixed Hodge modules and the Saito vanishing theorem.<br />
|-<br />
| bgcolor="#E0E0E0" | November 1<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | November 8<br />
| bgcolor="#C6D46E" |Ivan Aidun<br />
| bgcolor="#BCE2FE" |What is ... a Divisor?<br />
| bgcolor="#BCE2FE" |An elementary talk aimed at exploring the geometric and algebraic intuition for divisors, line bundles, and how they get used in Algebraic Geoemtry.<br />
|-<br />
| bgcolor="#E0E0E0" | November 15<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 22<br />
| bgcolor="#C6D46E" |Alex Mine<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 29<br />
| bgcolor="#C6D46E" |Yanbo Chen<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | December 9<br />
| bgcolor="#C6D46E" | Kevin Dao<br />
| bgcolor="#BCE2FE" |Basics on D-Modules<br />
| bgcolor="#BCE2FE" |This talk is my way to force myself to learn the basics of D-modules. The talk should be mostly accessible to first years and second years.<br />
|-<br />
| bgcolor="#E0E0E0" | December 13<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
| bgcolor="#BCE2FE" |<br />
|}<br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023] <br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022] [https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022] <br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25397Graduate Algebraic Geometry Seminar Fall 20232023-10-08T14:46:31Z<p>Jcobb2: /* Talks */</p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' Van Vleck B119<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/fNgXzpn7QAJM4Ybo9 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="200" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="200" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
| bgcolor="#BCD2EE" width="400" align="center" |'''Abstract'''<br />
|-<br />
| bgcolor="#E0E0E0" |September 13<br />
| bgcolor="#C6D46E" | Peter Wei<br />
| bgcolor="#BCE2FE" | Introduction to the Cartier Isomorphism (Pretalk)<br />
| bgcolor="#BCE2FE" | This is a preparatory talk for Josh Mundinger's talk on Friday. We discuss the Cartier isomorphism. <br />
|-<br />
| bgcolor="#E0E0E0" |September 20<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |September 27<br />
| bgcolor="#C6D46E" |Yifan Wei<br />
| bgcolor="#BCE2FE" |p-torsions in the p-adic land and de Rham cohomology<br />
| bgcolor="#BCE2FE" | Following Tate, we will try to visualize an elliptic curve over Cp, specifically, the p-adic disk near identity. Logarithm in the p-adic land provides a nice linearization to the problem, and we'll explore what this all means. If time permits, I'll sketch the proof of Hodge-Tate decomposition. (You know something like this is coming.)<br />
|-<br />
| bgcolor="#E0E0E0" |October 4<br />
| bgcolor="#C6D46E" |Owen Goff<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 11<br />
| bgcolor="#C6D46E" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 18<br />
| bgcolor="#C6D46E" |Alex Hof<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" | October 25<br />
| bgcolor="#C6D46E" |Jack Messina<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 1<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | November 8<br />
| bgcolor="#C6D46E" |Kevin Dao<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 15<br />
| bgcolor="#C6D46E" |Ivan Aidun<br />
| bgcolor="#BCE2FE" |My Summer Book Report on the Minimal Model Program<br />
| bgcolor="#BCE2FE" |What the hell is the Minimal Model Program? This summer, against my will, I learned. Now, you must too.<br />
|-<br />
| bgcolor="#E0E0E0" |November 22<br />
| bgcolor="#C6D46E" |Alex Mine<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 29<br />
| bgcolor="#C6D46E" |Yanbo Chen<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | December 9<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | December 13<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
| bgcolor="#BCE2FE" |<br />
|}<br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023] <br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022] [https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022] <br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25320Graduate Algebraic Geometry Seminar Fall 20232023-09-26T01:36:28Z<p>Jcobb2: /* Talks */</p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' Van Vleck B119<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/fNgXzpn7QAJM4Ybo9 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="200" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="200" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
| bgcolor="#BCD2EE" width="400" align="center" |'''Abstract'''<br />
|-<br />
| bgcolor="#E0E0E0" |September 13<br />
| bgcolor="#C6D46E" | Peter Wei<br />
| bgcolor="#BCE2FE" | Introduction to the Cartier Isomorphism (Pretalk)<br />
| bgcolor="#BCE2FE" | This is a preparatory talk for Josh Mundinger's talk on Friday. We discuss the Cartier isomorphism. <br />
|-<br />
| bgcolor="#E0E0E0" |September 20<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |September 27<br />
| bgcolor="#C6D46E" |Yifan Wei<br />
| bgcolor="#BCE2FE" |p-torsions in the p-adic land and de Rham cohomology<br />
| bgcolor="#BCE2FE" | Following Tate, we will try to visualize an elliptic curve over Cp, specifically, the p-adic disk near identity. Logarithm in the p-adic land provides a nice linearization to the problem, and we'll explore what this all means. If time permits, I'll sketch the proof of Hodge-Tate decomposition. (You know something like this is coming.)<br />
|-<br />
| bgcolor="#E0E0E0" |October 4<br />
| bgcolor="#C6D46E" |Owen Goff<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 11<br />
| bgcolor="#C6D46E" | Alex Mine<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 18<br />
| bgcolor="#C6D46E" |Alex Hof<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" | October 25<br />
| bgcolor="#C6D46E" |Jack Messina<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 1<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | November 8<br />
| bgcolor="#C6D46E" |Kevin Dao<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 15<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 22<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 29<br />
| bgcolor="#C6D46E" |Yanbo Chen<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | December 9<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | December 13<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
| bgcolor="#BCE2FE" |<br />
|}<br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023] <br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022] [https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022] <br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25262Graduate Algebraic Geometry Seminar Fall 20232023-09-19T15:19:13Z<p>Jcobb2: /* Wishlist */</p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' Van Vleck B119<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/fNgXzpn7QAJM4Ybo9 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="200" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="200" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
| bgcolor="#BCD2EE" width="400" align="center" |'''Abstract'''<br />
|-<br />
| bgcolor="#E0E0E0" |September 13<br />
| bgcolor="#C6D46E" | Peter Wei<br />
| bgcolor="#BCE2FE" | Introduction to the Cartier Isomorphism (Pretalk)<br />
| bgcolor="#BCE2FE" | This is a preparatory talk for Josh Mundinger's talk on Friday. We discuss the Cartier isomorphism. <br />
|-<br />
| bgcolor="#E0E0E0" |September 20<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |September 27<br />
| bgcolor="#C6D46E" |Yifan Wei<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 4<br />
| bgcolor="#C6D46E" |Owen Goff<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 11<br />
| bgcolor="#C6D46E" | Alex Mine<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 18<br />
| bgcolor="#C6D46E" |Alex Hof<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" | October 25<br />
| bgcolor="#C6D46E" |Jack Messina<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 1<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | November 8<br />
| bgcolor="#C6D46E" |Kevin Dao<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 15<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 22<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 29<br />
| bgcolor="#C6D46E" |Yanbo Chen<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | December 9<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | December 13<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
| bgcolor="#BCE2FE" |<br />
|}<br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023] <br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022] [https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022] <br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Fall_2023&diff=25255Directed Reading Program Fall 20232023-09-18T18:47:44Z<p>Jcobb2: /* Applications */</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, December 6th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are closed.<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
{| class="wikitable"<br />
|+Fall 2023 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Analysis On Graphs<br />
|We will study analysis on graphs. More precisely, we will read the book ''Introduction to Analysis on Graphs'' by Alexander Grigor'yan. The purpose of the book is to provide an introduction to the subject of the discrete Laplace operator on locally finite graphs. Analysis on graphs is a subject studies classical calculus and differential equations on discrete objects such as graphs. It has connections with many other important areas in math and outside of math. <br />
|Students should be familiar with basic calculus (221, 222 and 234) and linear algebra. Analysis courses such as 521 and 522 or basic probability theory are helpful.<br />
|-<br />
|Analysis, Geometry, and Combinatorics<br />
|I am very flexible and happy to work with your backgrounds and interests. A few things I've thought about are:<br />
<br />
- Looking at Guth's book "Polynomial Method's in Combinatorics", hopefully culminating in understanding the proof of the finite field Kakeya conjecture. <br />
<br />
- Measure theory - we'll start with Stein & Shakarchi's book, depending on how that goes, we could move on to Frank Morgan's "Geometric Measure Theory: A Beginner’s Guide" for a bit of geometric measure theory.<br />
<br />
- Laszlo Lovasz's book "Combinatorial Problems and Exercises". The name is pretty self-explanatory - this books balances more towards problems and less towards theory, but won't require much background.<br />
<br />
- Spivak's book "Calculus on manifolds". This isn't your usual calculus book - it will introduce differential forms, which are very useful in geometry and analysis. <br />
|-<br />
|Fractal geometry<br />
|In recent years, a surprising connection between two seemingly unrelated branches of math has emerged. Fractal dimension is a notion of size for sets which, unlike how we normally think about dimension, is not necessarily an integer (e.g. the rough shape of a coastline, the branching of a bolt of lightning, or the chaotic movement of a stock's price have non-integer dimension). Kolmogorov complexity, which measures how much information a string contains, can be applied to characterize some types of fractal dimension. This connection has already yielded impressive new results about fractal sets. <br />
In this DRP, we will start by understanding notions of fractal dimension and the definition/properties of Kolmogorov complexity. Then, we'll bridge the gap between the two via "effective" dimension. Effective dimension gives rise to elegant characterizations of both Hausdorff and packing dimension via the recently proven point-to-set principle, which we will study. Finally, we'll see some applications of this alternative definition, which makes it one of the most powerful new tools in fractal geometry. <br />
|I would like students who have taken 521-522. But I'm flexible and happy to find something which you feel ready for.<br />
|-<br />
|Number theory and Partition Theory<br />
|We will investigate modular forms with a view towards algebraic combinatorics and number theory. In this project, we will first read about the interesting connections of modular forms and number theory/arithmetic geometry, with a focus on the theory of theta functions and elliptic curves. We will then transition to a more concrete application of modular forms via partition theory. In particular, we'll cover both analytic and combinatorial techniques, such as the circle method and enumerative combinatorics. We may also dive into more modern applications such as mock theta functions. Depending on participant interest this may turn into a research project based on prior work of the mentor on generalizing the Rogers-Ramanujan identities in partition theory. <br />
|Students should have completed a semester of algebra (541) and be familiar with proofs. Familiarity with complex analysis will be useful though not required. Coding knowledge with python would also be useful. <br />
|-<br />
|Measure Theory<br />
|Euclidean space may seem simple enough, but it contains many complicated subsets with highly counterintuitive properties. Throughout the semester, we'll consider a number of examples of such subsets, including the standard Cantor set, fat and thin Cantor sets, Vitali sets, "large" meager sets, purely unrectifiable sets, Kakeya sets, Nikodym sets, and many more. Readings will be provided and will come from a variety of sources, <br />
|Students should either have taken 521 or currently be enrolled in it. <br />
|-<br />
|Basics of D-modules<br />
|In this project, students will be introduced to D-modules, which allow us to think about ideas from calculus, such as derivatives and differential equations, in an algebraic context. The topics covered will include the Weyl algebra, the Jacobian conjecture, rings of differential operators, modules over the Weyl algebra, and differential equations. The text we will use is "A Primer of Algebraic D-modules" by S.C. Coutinho.<br />
|The prerequisite is math 541 or an equivalent: rings, ideals, homomorphisms, polynomial rings, and abstract vector spaces. A basic knowledge of modules is necessary, but this can be introduced at the beginning of the project.<br />
|-<br />
|Commutative Algebra<br />
|Ideals, Varieties, and Algorithms (Chapters 1-2) with a view toward algebraic geometry.Students are expected to give "mini-talks" on the board for the section we read that week. <br />
|Some knowledge of abstract algebra but not much else.<br />
|-<br />
|Computability Theory, or, Algebra<br />
|1, Computability Theory: we will focus on computability theory, complexity theory, and cryptography. There is a book called Computational Complexity: A Moder Approach, and we can pay more attention to Non-determinism and NP Completeness. <br />
<br />
2, Algebra: we will focus on Linear Representations of Finite Groups. It is also the name of a book which describes the correspondence, due to Frobenius, between linear representations and characters. The book says this is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics and have tried to give proofs as elementary as possible, using only the definition of a group and the rudiments of linear algebra.<br />
|Strong abilities of Analysis and Discrete Mathematics (including Algebra, etc)<br />
|-<br />
|Machine Learning<br />
| In this project, students will read/watch parts of the "Practical Deep Learning for Coders" course of fast.ai, a deep learning library that aims to make deep learning as accessible as possible, with the aim of training a basic machine learning model of their own design. In parallel, the students will also develop the skills for some software development practices, such as unit testing, documentation, and key bindings.<br />
|Calculus, Linear Algebra, and basic programming experience (preferably including Python) are required. I would also like the students to be mostly independent as designing their own machine learning model is a goal for this project (although this goal is not a hard requirement) and as I might be away for some weeks during the semester.<br />
|-<br />
|Dynamics (Analysis/Geometry)<br />
|Ergodic theory studies dynamical systems (we can think of this as a repeated action) and their statistical properties (i.e. time averages). For example, consider a circle and pick a point and an angle. Now our action will be repeatedly rotating the point by the chosen angle. Now if we do this action repeatedly for a long time, what will the resulting orbit of the point be? Will it miss part of the circle? Go everywhere? Go everywhere equally often? If we choose an irrational angle the last is true and we call the system ergodic. Ergodic theory is concerned with the study of these systems. While we won’t directly study them, ergodic theory has applications in many other fields -- including number theory, harmonic analysis, probability, and mathematical physics -- making it an incredibly exciting multi-disciplinary area to study. Our plan will be to first spend some time reviewing measure theory, then look at some examples and define ergodicity rigorously. After that we will spend some time studying the various ergodic theorems. If time allows we will extend our study to mixing and entropy.<br />
|The Real Analysis sequence (or equivalent) is required. Having seen some measure theory will be extremely helpful though we will spend the first week or two reviewing this topic. Any geometry/topology is useful but not at all required.<br />
|}</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Fall_2023&diff=25254Directed Reading Program Fall 20232023-09-18T18:34:31Z<p>Jcobb2: /* Projects */</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, December 6th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are open until Friday, September 15th. [https://forms.gle/hNqf3JUN5kxb1xQ48 Click here]<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
{| class="wikitable"<br />
|+Fall 2023 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Analysis On Graphs<br />
|We will study analysis on graphs. More precisely, we will read the book ''Introduction to Analysis on Graphs'' by Alexander Grigor'yan. The purpose of the book is to provide an introduction to the subject of the discrete Laplace operator on locally finite graphs. Analysis on graphs is a subject studies classical calculus and differential equations on discrete objects such as graphs. It has connections with many other important areas in math and outside of math. <br />
|Students should be familiar with basic calculus (221, 222 and 234) and linear algebra. Analysis courses such as 521 and 522 or basic probability theory are helpful.<br />
|-<br />
|Analysis, Geometry, and Combinatorics<br />
|I am very flexible and happy to work with your backgrounds and interests. A few things I've thought about are:<br />
<br />
- Looking at Guth's book "Polynomial Method's in Combinatorics", hopefully culminating in understanding the proof of the finite field Kakeya conjecture. <br />
<br />
- Measure theory - we'll start with Stein & Shakarchi's book, depending on how that goes, we could move on to Frank Morgan's "Geometric Measure Theory: A Beginner’s Guide" for a bit of geometric measure theory.<br />
<br />
- Laszlo Lovasz's book "Combinatorial Problems and Exercises". The name is pretty self-explanatory - this books balances more towards problems and less towards theory, but won't require much background.<br />
<br />
- Spivak's book "Calculus on manifolds". This isn't your usual calculus book - it will introduce differential forms, which are very useful in geometry and analysis. <br />
|-<br />
|Fractal geometry<br />
|In recent years, a surprising connection between two seemingly unrelated branches of math has emerged. Fractal dimension is a notion of size for sets which, unlike how we normally think about dimension, is not necessarily an integer (e.g. the rough shape of a coastline, the branching of a bolt of lightning, or the chaotic movement of a stock's price have non-integer dimension). Kolmogorov complexity, which measures how much information a string contains, can be applied to characterize some types of fractal dimension. This connection has already yielded impressive new results about fractal sets. <br />
In this DRP, we will start by understanding notions of fractal dimension and the definition/properties of Kolmogorov complexity. Then, we'll bridge the gap between the two via "effective" dimension. Effective dimension gives rise to elegant characterizations of both Hausdorff and packing dimension via the recently proven point-to-set principle, which we will study. Finally, we'll see some applications of this alternative definition, which makes it one of the most powerful new tools in fractal geometry. <br />
|I would like students who have taken 521-522. But I'm flexible and happy to find something which you feel ready for.<br />
|-<br />
|Number theory and Partition Theory<br />
|We will investigate modular forms with a view towards algebraic combinatorics and number theory. In this project, we will first read about the interesting connections of modular forms and number theory/arithmetic geometry, with a focus on the theory of theta functions and elliptic curves. We will then transition to a more concrete application of modular forms via partition theory. In particular, we'll cover both analytic and combinatorial techniques, such as the circle method and enumerative combinatorics. We may also dive into more modern applications such as mock theta functions. Depending on participant interest this may turn into a research project based on prior work of the mentor on generalizing the Rogers-Ramanujan identities in partition theory. <br />
|Students should have completed a semester of algebra (541) and be familiar with proofs. Familiarity with complex analysis will be useful though not required. Coding knowledge with python would also be useful. <br />
|-<br />
|Measure Theory<br />
|Euclidean space may seem simple enough, but it contains many complicated subsets with highly counterintuitive properties. Throughout the semester, we'll consider a number of examples of such subsets, including the standard Cantor set, fat and thin Cantor sets, Vitali sets, "large" meager sets, purely unrectifiable sets, Kakeya sets, Nikodym sets, and many more. Readings will be provided and will come from a variety of sources, <br />
|Students should either have taken 521 or currently be enrolled in it. <br />
|-<br />
|Basics of D-modules<br />
|In this project, students will be introduced to D-modules, which allow us to think about ideas from calculus, such as derivatives and differential equations, in an algebraic context. The topics covered will include the Weyl algebra, the Jacobian conjecture, rings of differential operators, modules over the Weyl algebra, and differential equations. The text we will use is "A Primer of Algebraic D-modules" by S.C. Coutinho.<br />
|The prerequisite is math 541 or an equivalent: rings, ideals, homomorphisms, polynomial rings, and abstract vector spaces. A basic knowledge of modules is necessary, but this can be introduced at the beginning of the project.<br />
|-<br />
|Commutative Algebra<br />
|Ideals, Varieties, and Algorithms (Chapters 1-2) with a view toward algebraic geometry.Students are expected to give "mini-talks" on the board for the section we read that week. <br />
|Some knowledge of abstract algebra but not much else.<br />
|-<br />
|Computability Theory, or, Algebra<br />
|1, Computability Theory: we will focus on computability theory, complexity theory, and cryptography. There is a book called Computational Complexity: A Moder Approach, and we can pay more attention to Non-determinism and NP Completeness. <br />
<br />
2, Algebra: we will focus on Linear Representations of Finite Groups. It is also the name of a book which describes the correspondence, due to Frobenius, between linear representations and characters. The book says this is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics and have tried to give proofs as elementary as possible, using only the definition of a group and the rudiments of linear algebra.<br />
|Strong abilities of Analysis and Discrete Mathematics (including Algebra, etc)<br />
|-<br />
|Machine Learning<br />
| In this project, students will read/watch parts of the "Practical Deep Learning for Coders" course of fast.ai, a deep learning library that aims to make deep learning as accessible as possible, with the aim of training a basic machine learning model of their own design. In parallel, the students will also develop the skills for some software development practices, such as unit testing, documentation, and key bindings.<br />
|Calculus, Linear Algebra, and basic programming experience (preferably including Python) are required. I would also like the students to be mostly independent as designing their own machine learning model is a goal for this project (although this goal is not a hard requirement) and as I might be away for some weeks during the semester.<br />
|-<br />
|Dynamics (Analysis/Geometry)<br />
|Ergodic theory studies dynamical systems (we can think of this as a repeated action) and their statistical properties (i.e. time averages). For example, consider a circle and pick a point and an angle. Now our action will be repeatedly rotating the point by the chosen angle. Now if we do this action repeatedly for a long time, what will the resulting orbit of the point be? Will it miss part of the circle? Go everywhere? Go everywhere equally often? If we choose an irrational angle the last is true and we call the system ergodic. Ergodic theory is concerned with the study of these systems. While we won’t directly study them, ergodic theory has applications in many other fields -- including number theory, harmonic analysis, probability, and mathematical physics -- making it an incredibly exciting multi-disciplinary area to study. Our plan will be to first spend some time reviewing measure theory, then look at some examples and define ergodicity rigorously. After that we will spend some time studying the various ergodic theorems. If time allows we will extend our study to mixing and entropy.<br />
|The Real Analysis sequence (or equivalent) is required. Having seen some measure theory will be extremely helpful though we will spend the first week or two reviewing this topic. Any geometry/topology is useful but not at all required.<br />
|}</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Fall_2023&diff=25253Directed Reading Program Fall 20232023-09-18T18:34:05Z<p>Jcobb2: /* Projects */</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, December 6th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are open until Friday, September 15th. [https://forms.gle/hNqf3JUN5kxb1xQ48 Click here]<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
{| class="wikitable"<br />
|+Fall 2023 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Analysis On Graphs<br />
|We will study analysis on graphs. More precisely, we will read the book ''Introduction to Analysis on Graphs'' by Alexander Grigor'yan. The purpose of the book is to provide an introduction to the subject of the discrete Laplace operator on locally finite graphs. Analysis on graphs is a subject studies classical calculus and differential equations on discrete objects such as graphs. It has connections with many other important areas in math and outside of math. <br />
|Students should be familiar with basic calculus (221, 222 and 234) and linear algebra. Analysis courses such as 521 and 522 or basic probability theory are helpful.<br />
|-<br />
|Analysis, Geometry, and Combinatorics<br />
|I am very flexible and happy to work with your backgrounds and interests. A few things I've thought about are:<br />
<br />
- Looking at Guth's book "Polynomial Method's in Combinatorics", hopefully culminating in understanding the proof of the finite field Kakeya conjecture. <br />
<br />
- Measure theory - we'll start with Stein & Shakarchi's book, depending on how that goes, we could move on to Frank Morgan's "Geometric Measure Theory: A Beginner’s Guide" for a bit of geometric measure theory.<br />
<br />
- Laszlo Lovasz's book "Combinatorial Problems and Exercises". The name is pretty self-explanatory - this books balances more towards problems and less towards theory, but won't require much background.<br />
<br />
- Spivak's book "Calculus on manifolds". This isn't your usual calculus book - it will introduce differential forms, which are very useful in geometry and analysis. <br />
|-<br />
|Fractal geometry<br />
|In recent years, a surprising connection between two seemingly unrelated branches of math has emerged. Fractal dimension is a notion of size for sets which, unlike how we normally think about dimension, is not necessarily an integer (e.g. the rough shape of a coastline, the branching of a bolt of lightning, or the chaotic movement of a stock's price have non-integer dimension). Kolmogorov complexity, which measures how much information a string contains, can be applied to characterize some types of fractal dimension. This connection has already yielded impressive new results about fractal sets. <br />
In this DRP, we will start by understanding notions of fractal dimension and the definition/properties of Kolmogorov complexity. Then, we'll bridge the gap between the two via "effective" dimension. Effective dimension gives rise to elegant characterizations of both Hausdorff and packing dimension via the recently proven point-to-set principle, which we will study. Finally, we'll see some applications of this alternative definition, which makes it one of the most powerful new tools in fractal geometry. <br />
|I would like students who have taken 521-522. But I'm flexible and happy to find something which you feel ready for.<br />
|-<br />
|Number theory and Partition Theory<br />
|We will investigate modular forms with a view towards algebraic combinatorics and number theory. In this project, we will first read about the interesting connections of modular forms and number theory/arithmetic geometry, with a focus on the theory of theta functions and elliptic curves. We will then transition to a more concrete application of modular forms via partition theory. In particular, we'll cover both analytic and combinatorial techniques, such as the circle method and enumerative combinatorics. We may also dive into more modern applications such as mock theta functions. Depending on participant interest this may turn into a research project based on prior work of the mentor on generalizing the Rogers-Ramanujan identities in partition theory. <br />
|Students should have completed a semester of algebra (541) and be familiar with proofs. Familiarity with complex analysis will be useful though not required. Coding knowledge with python would also be useful. <br />
|-<br />
|Measure Theory<br />
|Euclidean space may seem simple enough, but it contains many complicated subsets with highly counterintuitive properties. Throughout the semester, we'll consider a number of examples of such subsets, including the standard Cantor set, fat and thin Cantor sets, Vitali sets, "large" meager sets, purely unrectifiable sets, Kakeya sets, Nikodym sets, and many more. Readings will be provided and will come from a variety of sources, <br />
|Students should either have taken 521 or currently be enrolled in it. <br />
|-<br />
|Basics of D-modules<br />
|In this project, students will be introduced to D-modules, which allow us to think about ideas from calculus, such as derivatives and differential equations, in an algebraic context. The topics covered will include the Weyl algebra, the Jacobian conjecture, rings of differential operators, modules over the Weyl algebra, and differential equations. The text we will use is "A Primer of Algebraic D-modules" by S.C. Coutinho.<br />
|The prerequisite is math 541 or an equivalent: rings, ideals, homomorphisms, polynomial rings, and abstract vector spaces. A basic knowledge of modules is necessary, but this can be introduced at the beginning of the project.<br />
|-<br />
|Elliptic Curves<br />
|We would like to acquire the basics of elliptic curves, and if time allows, we will finish with the statement of the Birch-Swinnerton-Dyer conjecture. In the meetings, students will have a chance to take turns and teach the rest of the group a summary of the material in the textbook.<br />
|Knowledge in Calculus, Linear algebra, and Abstract Algebra is recommended.<br />
|-<br />
|Commutative Algebra<br />
|Ideals, Varieties, and Algorithms (Chapters 1-2) with a view toward algebraic geometry.Students are expected to give "mini-talks" on the board for the section we read that week. <br />
|Some knowledge of abstract algebra but not much else.<br />
|-<br />
|Computability Theory, or, Algebra<br />
|1, Computability Theory: we will focus on computability theory, complexity theory, and cryptography. There is a book called Computational Complexity: A Moder Approach, and we can pay more attention to Non-determinism and NP Completeness. <br />
<br />
2, Algebra: we will focus on Linear Representations of Finite Groups. It is also the name of a book which describes the correspondence, due to Frobenius, between linear representations and characters. The book says this is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics and have tried to give proofs as elementary as possible, using only the definition of a group and the rudiments of linear algebra.<br />
|Strong abilities of Analysis and Discrete Mathematics (including Algebra, etc)<br />
|-<br />
|Machine Learning<br />
| In this project, students will read/watch parts of the "Practical Deep Learning for Coders" course of fast.ai, a deep learning library that aims to make deep learning as accessible as possible, with the aim of training a basic machine learning model of their own design. In parallel, the students will also develop the skills for some software development practices, such as unit testing, documentation, and key bindings.<br />
|Calculus, Linear Algebra, and basic programming experience (preferably including Python) are required. I would also like the students to be mostly independent as designing their own machine learning model is a goal for this project (although this goal is not a hard requirement) and as I might be away for some weeks during the semester.<br />
|-<br />
|Dynamics (Analysis/Geometry)<br />
|Ergodic theory studies dynamical systems (we can think of this as a repeated action) and their statistical properties (i.e. time averages). For example, consider a circle and pick a point and an angle. Now our action will be repeatedly rotating the point by the chosen angle. Now if we do this action repeatedly for a long time, what will the resulting orbit of the point be? Will it miss part of the circle? Go everywhere? Go everywhere equally often? If we choose an irrational angle the last is true and we call the system ergodic. Ergodic theory is concerned with the study of these systems. While we won’t directly study them, ergodic theory has applications in many other fields -- including number theory, harmonic analysis, probability, and mathematical physics -- making it an incredibly exciting multi-disciplinary area to study. Our plan will be to first spend some time reviewing measure theory, then look at some examples and define ergodicity rigorously. After that we will spend some time studying the various ergodic theorems. If time allows we will extend our study to mixing and entropy.<br />
|The Real Analysis sequence (or equivalent) is required. Having seen some measure theory will be extremely helpful though we will spend the first week or two reviewing this topic. Any geometry/topology is useful but not at all required.<br />
|}</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Fall_2023&diff=25252Directed Reading Program Fall 20232023-09-18T18:32:45Z<p>Jcobb2: /* Projects */</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, December 6th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are open until Friday, September 15th. [https://forms.gle/hNqf3JUN5kxb1xQ48 Click here]<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
{| class="wikitable"<br />
|+Fall 2023 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Analysis On Graphs<br />
|We will study analysis on graphs. More precisely, we will read the book ''Introduction to Analysis on Graphs'' by Alexander Grigor'yan. The purpose of the book is to provide an introduction to the subject of the discrete Laplace operator on locally finite graphs. Analysis on graphs is a subject studies classical calculus and differential equations on discrete objects such as graphs. It has connections with many other important areas in math and outside of math. <br />
|Students should be familiar with basic calculus (221, 222 and 234) and linear algebra. Analysis courses such as 521 and 522 or basic probability theory are helpful.<br />
|-<br />
|Analysis, Geometry, and Combinatorics<br />
|I am very flexible and happy to work with your backgrounds and interests. A few things I've thought about are:<br />
<br />
- Looking at Guth's book "Polynomial Method's in Combinatorics", hopefully culminating in understanding the proof of the finite field Kakeya conjecture. <br />
<br />
- Measure theory - we'll start with Stein & Shakarchi's book, depending on how that goes, we could move on to Frank Morgan's "Geometric Measure Theory: A Beginner’s Guide" for a bit of geometric measure theory.<br />
<br />
- Laszlo Lovasz's book "Combinatorial Problems and Exercises". The name is pretty self-explanatory - this books balances more towards problems and less towards theory, but won't require much background.<br />
<br />
- Spivak's book "Calculus on manifolds". This isn't your usual calculus book - it will introduce differential forms, which are very useful in geometry and analysis. <br />
|-<br />
|Fractal geometry<br />
|In recent years, a surprising connection between two seemingly unrelated branches of math has emerged. Fractal dimension is a notion of size for sets which, unlike how we normally think about dimension, is not necessarily an integer (e.g. the rough shape of a coastline, the branching of a bolt of lightning, or the chaotic movement of a stock's price have non-integer dimension). Kolmogorov complexity, which measures how much information a string contains, can be applied to characterize some types of fractal dimension. This connection has already yielded impressive new results about fractal sets. <br />
In this DRP, we will start by understanding notions of fractal dimension and the definition/properties of Kolmogorov complexity. Then, we'll bridge the gap between the two via "effective" dimension. Effective dimension gives rise to elegant characterizations of both Hausdorff and packing dimension via the recently proven point-to-set principle, which we will study. Finally, we'll see some applications of this alternative definition, which makes it one of the most powerful new tools in fractal geometry. <br />
|I would like students who have taken 521-522. But I'm flexible and happy to find something which you feel ready for.<br />
|-<br />
|Number theory and Partition Theory<br />
|We will investigate modular forms with a view towards algebraic combinatorics and number theory. In this project, we will first read about the interesting connections of modular forms and number theory/arithmetic geometry, with a focus on the theory of theta functions and elliptic curves. We will then transition to a more concrete application of modular forms via partition theory. In particular, we'll cover both analytic and combinatorial techniques, such as the circle method and enumerative combinatorics. We may also dive into more modern applications such as mock theta functions. Depending on participant interest this may turn into a research project based on prior work of the mentor on generalizing the Rogers-Ramanujan identities in partition theory. <br />
|Students should have completed a semester of algebra (541) and be familiar with proofs. Familiarity with complex analysis will be useful though not required. Coding knowledge with python would also be useful. <br />
|-<br />
|Measure Theory<br />
|Euclidean space may seem simple enough, but it contains many complicated subsets with highly counterintuitive properties. Throughout the semester, we'll consider a number of examples of such subsets, including the standard Cantor set, fat and thin Cantor sets, Vitali sets, "large" meager sets, purely unrectifiable sets, Kakeya sets, Nikodym sets, and many more. Readings will be provided and will come from a variety of sources, <br />
|Students should either have taken 521 or currently be enrolled in it. <br />
|-<br />
|Basics of D-modules<br />
|In this project, students will be introduced to D-modules, which allow us to think about ideas from calculus, such as derivatives and differential equations, in an algebraic context. The topics covered will include the Weyl algebra, the Jacobian conjecture, rings of differential operators, modules over the Weyl algebra, and differential equations. The text we will use is "A Primer of Algebraic D-modules" by S.C. Coutinho.<br />
|The prerequisite is math 541 or an equivalent: rings, ideals, homomorphisms, polynomial rings, and abstract vector spaces. A basic knowledge of modules is necessary, but this can be introduced at the beginning of the project.<br />
|-<br />
|Elliptic Curves<br />
|We would like to acquire the basics of elliptic curves, and if time allows, we will finish with the statement of the Birch-Swinnerton-Dyer conjecture. In the meetings, students will have a chance to take turns and teach the rest of the group a summary of the material in the textbook.<br />
|Knowledge in Calculus, Linear algebra, and Abstract Algebra is recommended.<br />
|-<br />
|Commutative Algebra<br />
|Ideals, Varieties, and Algorithms (Chapters 1-2) with a view toward algebraic geometry.Students are expected to give "mini-talks" on the board for the section we read that week. <br />
|Some knowledge of abstract algebra but not much else.<br />
|-<br />
|Computability Theory, or, Algebra<br />
|1, Computability Theory: we will focus on computability theory, complexity theory, and cryptography. There is a book called Computational Complexity: A Moder Approach, and we can pay more attention to Non-determinism and NP Completeness. <br />
<br />
2, Algebra: we will focus on Linear Representations of Finite Groups. It is also the name of a book which describes the correspondence, due to Frobenius, between linear representations and characters. The book says this is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics and have tried to give proofs as elementary as possible, using only the definition of a group and the rudiments of linear algebra.<br />
|Strong abilities of Analysis and Discrete Mathematics (including Algebra, etc)<br />
|-<br />
|Machine Learning<br />
| In this project, students will read/watch parts of the "Practical Deep Learning for Coders" course of fast.ai, a deep learning library that aims to make deep learning as accessible as possible, with the aim of training a basic machine learning model of their own design. In parallel, the students will also develop the skills for some software development practices, such as unit testing, documentation, and key bindings.<br />
|Calculus, Linear Algebra, and basic programming experience (preferably including Python) are required. I would also like the students to be mostly independent as designing their own machine learning model is a goal for this project (although this goal is not a hard requirement) and as I might be away for some weeks during the semester.<br />
|-<br />
|Dynamics (Analysis/Geometry)<br />
|Ergodic theory studies dynamical systems (we can think of this as a repeated action) and their statistical properties (i.e. time averages). For example, consider a circle and pick a point and an angle. Now our action will be repeatedly rotating the point by the chosen angle. Now if we do this action repeatedly for a long time, what will the resulting orbit of the point be? Will it miss part of the circle? Go everywhere? Go everywhere equally often? If we choose an irrational angle the last is true and we call the system ergodic. Ergodic theory is concerned with the study of these systems. While we won’t directly study them, ergodic theory has applications in many other fields -- including number theory, harmonic analysis, probability, and mathematical physics -- making it an incredibly exciting multi-disciplinary area to study. Our plan will be to first spend some time reviewing measure theory, then look at some examples and define ergodicity rigorously. After that we will spend some time studying the various ergodic theorems. If time allows we will extend our study to mixing and entropy.<br />
|The Real Analysis sequence (or equivalent) is required. Having seen some measure theory will be extremely helpful though we will spend the first week or two reviewing this topic. Any geometry/topology is useful but not at all required.<br />
|-<br />
| Algebra and Combinatorics<br />
| This project will cover the algebraic properties of graphs. When I say "graph" I mean "network of edges and vertices", and when I say "algebraic" I'm talking about groups and rings. They're interconnected in many ways from automorphisms to eigenvalues. This semester we will be reading "Algebraic Graph Theory" by Norman Biggs, and unlock many secrets.<br />
|Some familiarity with algebra (e.g. Math 541 -- you can take it simultaneously)<br />
|}</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25249Graduate Algebraic Geometry Seminar Fall 20232023-09-18T15:39:32Z<p>Jcobb2: /* Talks */</p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' Van Vleck B119<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/fNgXzpn7QAJM4Ybo9 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="200" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="200" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
| bgcolor="#BCD2EE" width="400" align="center" |'''Abstract'''<br />
|-<br />
| bgcolor="#E0E0E0" |September 13<br />
| bgcolor="#C6D46E" | Peter Wei<br />
| bgcolor="#BCE2FE" | Introduction to the Cartier Isomorphism (Pretalk)<br />
| bgcolor="#BCE2FE" | This is a preparatory talk for Josh Mundinger's talk on Friday. We discuss the Cartier isomorphism. <br />
|-<br />
| bgcolor="#E0E0E0" |September 20<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |September 27<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 4<br />
| bgcolor="#C6D46E" |Owen Goff<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 11<br />
| bgcolor="#C6D46E" | Alex Mine<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 18<br />
| bgcolor="#C6D46E" |Alex Hof<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" | October 25<br />
| bgcolor="#C6D46E" |Jack Messina<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 1<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | November 8<br />
| bgcolor="#C6D46E" |Kevin Dao<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 15<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 22<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 29<br />
| bgcolor="#C6D46E" |Yanbo Chen<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | December 9<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | December 13<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
| bgcolor="#BCE2FE" |<br />
|}<br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023] <br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022] [https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022] <br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25215Graduate Algebraic Geometry Seminar Fall 20232023-09-12T22:09:57Z<p>Jcobb2: </p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' Van Vleck B119<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/fNgXzpn7QAJM4Ybo9 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="200" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="200" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
| bgcolor="#BCD2EE" width="400" align="center" |'''Abstract'''<br />
|-<br />
| bgcolor="#E0E0E0" |September 13<br />
| bgcolor="#C6D46E" | Peter Wei<br />
| bgcolor="#BCE2FE" | Introduction to the Cartier Isomorphism (Pretalk)<br />
| bgcolor="#BCE2FE" | This is a preparatory talk for Josh Mundinger's talk on Friday. We discuss the Cartier isomorphism. <br />
|-<br />
| bgcolor="#E0E0E0" |September 20<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |September 27<br />
| bgcolor="#C6D46E" |Owen Goff<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 4<br />
| bgcolor="#C6D46E" |Alex Mine<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 11<br />
| bgcolor="#C6D46E" | Alex Hof<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 18<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | October 25<br />
| bgcolor="#C6D46E" |Jack Messina<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 1<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | November 8<br />
| bgcolor="#C6D46E" |Kevin Dao<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 15<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 22<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 29<br />
| bgcolor="#C6D46E" |Yanbo Chen<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | December 9<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | December 13<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
| bgcolor="#BCE2FE" |<br />
|}<br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023] <br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022] [https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022] <br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25213Graduate Algebraic Geometry Seminar Fall 20232023-09-12T15:32:20Z<p>Jcobb2: /* Past Semesters */</p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' TBA<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/XmdJ4hGbxvpbVVwr5 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="200" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="200" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
| bgcolor="#BCD2EE" width="400" align="center" |'''Abstract'''<br />
|-<br />
| bgcolor="#E0E0E0" |September 13<br />
| bgcolor="#C6D46E" | Peter Wei<br />
| bgcolor="#BCE2FE" | Introduction to the Cartier Isomorphism (Pretalk)<br />
| bgcolor="#BCE2FE" | This is a preparatory talk for Josh Mundinger's talk on Friday. We discuss the Cartier isomorphism. <br />
|-<br />
| bgcolor="#E0E0E0" |September 20<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |September 27<br />
| bgcolor="#C6D46E" |Owen Goff<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 4<br />
| bgcolor="#C6D46E" |Alex Mine<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 11<br />
| bgcolor="#C6D46E" | Alex Hof<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 18<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | October 25<br />
| bgcolor="#C6D46E" |Jack Messina<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 1<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | November 8<br />
| bgcolor="#C6D46E" |Kevin Dao<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 15<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 22<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 29<br />
| bgcolor="#C6D46E" |Yanbo Chen<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | December 9<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | December 13<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
| bgcolor="#BCE2FE" |<br />
|}<br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023] <br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022] [https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022] <br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016] [https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25212Graduate Algebraic Geometry Seminar Fall 20232023-09-12T15:31:36Z<p>Jcobb2: /* Talks */</p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' TBA<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/XmdJ4hGbxvpbVVwr5 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="200" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="200" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
| bgcolor="#BCD2EE" width="400" align="center" |'''Abstract'''<br />
|-<br />
| bgcolor="#E0E0E0" |September 13<br />
| bgcolor="#C6D46E" | Peter Wei<br />
| bgcolor="#BCE2FE" | Introduction to the Cartier Isomorphism (Pretalk)<br />
| bgcolor="#BCE2FE" | This is a preparatory talk for Josh Mundinger's talk on Friday. We discuss the Cartier isomorphism. <br />
|-<br />
| bgcolor="#E0E0E0" |September 20<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |September 27<br />
| bgcolor="#C6D46E" |Owen Goff<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 4<br />
| bgcolor="#C6D46E" |Alex Mine<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 11<br />
| bgcolor="#C6D46E" | Alex Hof<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 18<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | October 25<br />
| bgcolor="#C6D46E" |Jack Messina<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 1<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | November 8<br />
| bgcolor="#C6D46E" |Kevin Dao<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 15<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 22<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 29<br />
| bgcolor="#C6D46E" |Yanbo Chen<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | December 9<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | December 13<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
| bgcolor="#BCE2FE" |<br />
|}<br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25211Graduate Algebraic Geometry Seminar Fall 20232023-09-12T15:31:23Z<p>Jcobb2: /* Talks */</p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' TBA<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/XmdJ4hGbxvpbVVwr5 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="200" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="200" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
| bgcolor="#BCD2EE" width="400" align="center" |'''Abstract'''<br />
|-<br />
| bgcolor="#E0E0E0" |September 13<br />
| bgcolor="#C6D46E" | Peter Wei<br />
| bgcolor="#BCE2FE" | Introduction to the Cartier Isomorphism (Pretalk)<br />
| bgcolor="#BCE2FE" | This is a preparatory talk for Josh Mundinger's talk on Friday. We discuss the Cartier isomorphism. <br />
|-<br />
| bgcolor="#E0E0E0" |September 20<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |September 27<br />
| bgcolor="#C6D46E" |Owen Goff<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 4<br />
| bgcolor="#C6D46E" |Alex Mine<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |October 11<br />
| bgcolor="#C6D46E" | Alex Hof<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 18|October 18]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | October 25<br />
| bgcolor="#C6D46E" |Jack Messina<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 1<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | November 8<br />
| bgcolor="#C6D46E" |Kevin Dao<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 15<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 22<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 29<br />
| bgcolor="#C6D46E" |Yanbo Chen<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | December 9<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | December 13<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
| bgcolor="#BCE2FE" |<br />
|}<br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Fall_2023&diff=25174Directed Reading Program Fall 20232023-09-07T14:51:37Z<p>Jcobb2: Add projects</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, December 6th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are open until Friday, September 15th. [https://forms.gle/hNqf3JUN5kxb1xQ48 Click here]<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
{| class="wikitable"<br />
|+Spring 2023 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Analysis On Graphs<br />
|We will study analysis on graphs. More precisely, we will read the book ''Introduction to Analysis on Graphs'' by Alexander Grigor'yan. The purpose of the book is to provide an introduction to the subject of the discrete Laplace operator on locally finite graphs. Analysis on graphs is a subject studies classical calculus and differential equations on discrete objects such as graphs. It has connections with many other important areas in math and outside of math. <br />
|Students should be familiar with basic calculus (221, 222 and 234) and linear algebra. Analysis courses such as 521 and 522 or basic probability theory are helpful.<br />
|-<br />
|Analysis, Geometry, and Combinatorics<br />
|I am very flexible and happy to work with your backgrounds and interests. A few things I've thought about are:<br />
<br />
- Looking at Guth's book "Polynomial Method's in Combinatorics", hopefully culminating in understanding the proof of the finite field Kakeya conjecture. <br />
<br />
- Measure theory - we'll start with Stein & Shakarchi's book, depending on how that goes, we could move on to Frank Morgan's "Geometric Measure Theory: A Beginner’s Guide" for a bit of geometric measure theory.<br />
<br />
- Laszlo Lovasz's book "Combinatorial Problems and Exercises". The name is pretty self-explanatory - this books balances more towards problems and less towards theory, but won't require much background.<br />
<br />
- Spivak's book "Calculus on manifolds". This isn't your usual calculus book - it will introduce differential forms, which are very useful in geometry and analysis. <br />
|-<br />
|Fractal geometry<br />
|In recent years, a surprising connection between two seemingly unrelated branches of math has emerged. Fractal dimension is a notion of size for sets which, unlike how we normally think about dimension, is not necessarily an integer (e.g. the rough shape of a coastline, the branching of a bolt of lightning, or the chaotic movement of a stock's price have non-integer dimension). Kolmogorov complexity, which measures how much information a string contains, can be applied to characterize some types of fractal dimension. This connection has already yielded impressive new results about fractal sets. <br />
In this DRP, we will start by understanding notions of fractal dimension and the definition/properties of Kolmogorov complexity. Then, we'll bridge the gap between the two via "effective" dimension. Effective dimension gives rise to elegant characterizations of both Hausdorff and packing dimension via the recently proven point-to-set principle, which we will study. Finally, we'll see some applications of this alternative definition, which makes it one of the most powerful new tools in fractal geometry. <br />
|I would like students who have taken 521-522. But I'm flexible and happy to find something which you feel ready for.<br />
|-<br />
|Number theory and Partition Theory<br />
|We will investigate modular forms with a view towards algebraic combinatorics and number theory. In this project, we will first read about the interesting connections of modular forms and number theory/arithmetic geometry, with a focus on the theory of theta functions and elliptic curves. We will then transition to a more concrete application of modular forms via partition theory. In particular, we'll cover both analytic and combinatorial techniques, such as the circle method and enumerative combinatorics. We may also dive into more modern applications such as mock theta functions. Depending on participant interest this may turn into a research project based on prior work of the mentor on generalizing the Rogers-Ramanujan identities in partition theory. <br />
|Students should have completed a semester of algebra (541) and be familiar with proofs. Familiarity with complex analysis will be useful though not required. Coding knowledge with python would also be useful. <br />
|-<br />
|Measure Theory<br />
|Euclidean space may seem simple enough, but it contains many complicated subsets with highly counterintuitive properties. Throughout the semester, we'll consider a number of examples of such subsets, including the standard Cantor set, fat and thin Cantor sets, Vitali sets, "large" meager sets, purely unrectifiable sets, Kakeya sets, Nikodym sets, and many more. Readings will be provided and will come from a variety of sources, <br />
|Students should either have taken 521 or currently be enrolled in it. <br />
|-<br />
|Basics of D-modules<br />
|In this project, students will be introduced to D-modules, which allow us to think about ideas from calculus, such as derivatives and differential equations, in an algebraic context. The topics covered will include the Weyl algebra, the Jacobian conjecture, rings of differential operators, modules over the Weyl algebra, and differential equations. The text we will use is "A Primer of Algebraic D-modules" by S.C. Coutinho.<br />
|The prerequisite is math 541 or an equivalent: rings, ideals, homomorphisms, polynomial rings, and abstract vector spaces. A basic knowledge of modules is necessary, but this can be introduced at the beginning of the project.<br />
|-<br />
|Elliptic Curves<br />
|We would like to acquire the basics of elliptic curves, and if time allows, we will finish with the statement of the Birch-Swinnerton-Dyer conjecture. In the meetings, students will have a chance to take turns and teach the rest of the group a summary of the material in the textbook.<br />
|Knowledge in Calculus, Linear algebra, and Abstract Algebra is recommended.<br />
|-<br />
|Commutative Algebra<br />
|Ideals, Varieties, and Algorithms (Chapters 1-2) with a view toward algebraic geometry.Students are expected to give "mini-talks" on the board for the section we read that week. <br />
|Some knowledge of abstract algebra but not much else.<br />
|-<br />
|Computability Theory, or, Algebra<br />
|1, Computability Theory: we will focus on computability theory, complexity theory, and cryptography. There is a book called Computational Complexity: A Moder Approach, and we can pay more attention to Non-determinism and NP Completeness. <br />
<br />
2, Algebra: we will focus on Linear Representations of Finite Groups. It is also the name of a book which describes the correspondence, due to Frobenius, between linear representations and characters. The book says this is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics and have tried to give proofs as elementary as possible, using only the definition of a group and the rudiments of linear algebra.<br />
|Strong abilities of Analysis and Discrete Mathematics (including Algebra, etc)<br />
|-<br />
|Machine Learning<br />
| In this project, students will read/watch parts of the "Practical Deep Learning for Coders" course of fast.ai, a deep learning library that aims to make deep learning as accessible as possible, with the aim of training a basic machine learning model of their own design. In parallel, the students will also develop the skills for some software development practices, such as unit testing, documentation, and key bindings.<br />
|Calculus, Linear Algebra, and basic programming experience (preferably including Python) are required. I would also like the students to be mostly independent as designing their own machine learning model is a goal for this project (although this goal is not a hard requirement) and as I might be away for some weeks during the semester.<br />
|-<br />
|Dynamics (Analysis/Geometry)<br />
|Ergodic theory studies dynamical systems (we can think of this as a repeated action) and their statistical properties (i.e. time averages). For example, consider a circle and pick a point and an angle. Now our action will be repeatedly rotating the point by the chosen angle. Now if we do this action repeatedly for a long time, what will the resulting orbit of the point be? Will it miss part of the circle? Go everywhere? Go everywhere equally often? If we choose an irrational angle the last is true and we call the system ergodic. Ergodic theory is concerned with the study of these systems. While we won’t directly study them, ergodic theory has applications in many other fields -- including number theory, harmonic analysis, probability, and mathematical physics -- making it an incredibly exciting multi-disciplinary area to study. Our plan will be to first spend some time reviewing measure theory, then look at some examples and define ergodicity rigorously. After that we will spend some time studying the various ergodic theorems. If time allows we will extend our study to mixing and entropy.<br />
|The Real Analysis sequence (or equivalent) is required. Having seen some measure theory will be extremely helpful though we will spend the first week or two reviewing this topic. Any geometry/topology is useful but not at all required.<br />
|-<br />
| Algebra and Combinatorics<br />
| This project will cover the algebraic properties of graphs. When I say "graph" I mean "network of edges and vertices", and when I say "algebraic" I'm talking about groups and rings. They're interconnected in many ways from automorphisms to eigenvalues. This semester we will be reading "Algebraic Graph Theory" by Norman Biggs, and unlock many secrets.<br />
|Some familiarity with algebra (e.g. Math 541 -- you can take it simultaneously)<br />
|}</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Fall_2023&diff=25173Directed Reading Program Fall 20232023-09-07T14:42:20Z<p>Jcobb2: Fix applications on DRP website</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, December 6th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are open until Friday, September 15th. [https://forms.gle/hNqf3JUN5kxb1xQ48 Click here]<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
Coming soon...</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25162Graduate Algebraic Geometry Seminar Fall 20232023-09-06T18:34:33Z<p>Jcobb2: /* Talks */</p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' TBA<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/XmdJ4hGbxvpbVVwr5 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="200" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="200" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
| bgcolor="#BCD2EE" width="400" align="center" |'''Abstract'''<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 13|September 13]]<br />
| bgcolor="#C6D46E" | Peter Wei<br />
| bgcolor="#BCE2FE" | Introduction to the Cartier Isomorphism (Pretalk)<br />
| bgcolor="#BCE2FE" | This is a preparatory talk for Josh Mundinger's talk on Friday. We discuss the Cartier isomorphism. <br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 20|September 20]]<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 27|September 27]]<br />
| bgcolor="#C6D46E" |Owen Goff<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 4|October 4]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 11|October 11]]<br />
| bgcolor="#C6D46E" | Alex Hof<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 18|October 18]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | October 25<br />
| bgcolor="#C6D46E" |Jack Messina<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 1<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | November 8<br />
| bgcolor="#C6D46E" |Kevin Dao<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 15<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 22<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 29<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | December 9<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | December 13<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
| bgcolor="#BCE2FE" |<br />
|}<br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25161Graduate Algebraic Geometry Seminar Fall 20232023-09-06T18:33:36Z<p>Jcobb2: </p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' TBA<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/XmdJ4hGbxvpbVVwr5 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
| bgcolor="#BCD2EE" width="400" align="center" |'''Abstract'''<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 13|September 13]]<br />
| bgcolor="#C6D46E" | Peter Wei<br />
| bgcolor="#BCE2FE" | Introduction to the Cartier Isomorphism (Pretalk)<br />
| bgcolor="#BCE2FE" | This is a preparatory talk for Josh Mundinger's talk on Friday. We discuss the Cartier isomorphism. <br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 20|September 20]]<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 27|September 27]]<br />
| bgcolor="#C6D46E" |Owen Goff<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 4|October 4]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 11|October 11]]<br />
| bgcolor="#C6D46E" | Alex Hof<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 18|October 18]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | October 25<br />
| bgcolor="#C6D46E" |Jack Messina<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 1<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | November 8<br />
| bgcolor="#C6D46E" |Kevin Dao<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 15<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 22<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 29<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | December 9<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | December 13<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
| bgcolor="#BCE2FE" |<br />
|}<br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25160Graduate Algebraic Geometry Seminar Fall 20232023-09-06T18:33:16Z<p>Jcobb2: gags prep talk</p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' TBA<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/XmdJ4hGbxvpbVVwr5 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
| bgcolor="#BCD2EE" width="400" align="center" |'''Abstract'''<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 13|September 13]]<br />
| bgcolor="#C6D46E" | Peter Wei<br />
| bgcolor="#BCE2FE" | Introduction to the Cartier Isomorphism (Pretalk)<br />
| bgcolor="#BCE2FE" | This is a preparatory talk for Josh Mundinger's talk on Friday. We discuss the Cartier isomorphism. <br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 20|September 20]]<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 27|September 27]]<br />
| bgcolor="#C6D46E" |Owen Goff<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 4|October 4]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 11|October 11]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 18|October 18]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | October 25<br />
| bgcolor="#C6D46E" |Jack Messina<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 1<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | November 8<br />
| bgcolor="#C6D46E" |Kevin Dao<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 15<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 22<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 29<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | December 9<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | December 13<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
| bgcolor="#BCE2FE" |<br />
|}<br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25157Graduate Algebraic Geometry Seminar Fall 20232023-09-06T15:49:31Z<p>Jcobb2: /* Talks */</p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' TBA<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/XmdJ4hGbxvpbVVwr5 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
| bgcolor="#BCD2EE" width="400" align="center" |'''Abstract'''<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 13|September 13]]<br />
| bgcolor="#C6D46E" | Alex Hof<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 20|September 20]]<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 27|September 27]]<br />
| bgcolor="#C6D46E" |Owen Goff<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 4|October 4]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 11|October 11]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 18|October 18]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | October 25<br />
| bgcolor="#C6D46E" |Jack Messina<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 1<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | November 8<br />
| bgcolor="#C6D46E" |Kevin Dao<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 15<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 22<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 29<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | December 9<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | December 13<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
| bgcolor="#BCE2FE" |<br />
|}<br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25156Graduate Algebraic Geometry Seminar Fall 20232023-09-06T15:48:40Z<p>Jcobb2: /* Talks */ Remove all of the duplicate info, put in table</p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' TBA<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/XmdJ4hGbxvpbVVwr5 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
| bgcolor="#BCD2EE" width="400" align="center" |'''Abstract'''<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 13|September 13]]<br />
| bgcolor="#C6D46E" | Alex Hof<br />
| bgcolor="#BCE2FE" | TBA<br />
| bgcolor="#BCD2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 20|September 20]]<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCD2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 27|September 27]]<br />
| bgcolor="#C6D46E" |Owen Goff<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCD2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 4|October 4]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCD2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 11|October 11]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCD2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 18|October 18]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCD2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" | October 25<br />
| bgcolor="#C6D46E" |Jack Messina<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCD2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 1<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCD2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | November 8<br />
| bgcolor="#C6D46E" |Kevin Dao<br />
| bgcolor="#BCE2FE" |TBA<br />
| bgcolor="#BCD2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" | November 15<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 22<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |November 29<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | December 9<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" |<br />
| bgcolor="#BCD2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" | December 13<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
| bgcolor="#BCD2FE" | <br />
|}<br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25155Graduate Algebraic Geometry Seminar Fall 20232023-09-06T15:43:24Z<p>Jcobb2: talks</p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' TBA<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/XmdJ4hGbxvpbVVwr5 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 13|September 13]]<br />
| bgcolor="#C6D46E" | Alex Hof<br />
| bgcolor="#BCE2FE" | TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 20|September 20]]<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 27|September 27]]<br />
| bgcolor="#C6D46E" |Owen Goff<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 4|October 4]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 11|October 11]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 18|October 18]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 25|October 25]]<br />
| bgcolor="#C6D46E" |Jack Messina<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#November 1|November 1]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#November 8|November 8]]<br />
| bgcolor="#C6D46E" |Kevin Dao<br />
| bgcolor="#BCE2FE" |TBA<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#November 15|November 15]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#November 22| November 22]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#November 29|November 29]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#December 6|December 6]]<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#December 13|December 13]]<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
|}<br />
</center><br />
<br />
===September 13===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===September 20===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
<br />
===September 27===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===October 4===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><center></center><br />
<br />
===October 11===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
===October 18===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
<br />
===October 25===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===November 1===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===November 8===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===November 15===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
<br />
===November 22===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===November 29===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title:<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===December 6===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title:<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===December 13===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25115Graduate Algebraic Geometry Seminar Fall 20232023-09-04T16:38:43Z<p>Jcobb2: </p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' TBA<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/XmdJ4hGbxvpbVVwr5 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 13|September 13]]<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 20|September 20]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 27|September 27]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 4|October 4]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 11|October 11]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 18|October 18]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 25|October 25]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#November 1|November 1]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#November 8|November 8]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#November 15|November 15]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#November 22| November 22]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#November 29|November 29]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#December 6|December 6]]<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#December 13|December 13]]<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
|}<br />
</center><br />
<br />
===September 13===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===September 20===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
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|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
<br />
===September 27===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===October 4===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><center></center><br />
<br />
===October 11===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
===October 18===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
<br />
===October 25===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===November 1===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===November 8===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===November 15===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
<br />
===November 22===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===November 29===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title:<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===December 6===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title:<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===December 13===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25098Graduate Algebraic Geometry Seminar Fall 20232023-08-31T16:00:33Z<p>Jcobb2: blank out talks</p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' Van Vleck B119<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/XmdJ4hGbxvpbVVwr5 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 13|September 13]]<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 20|September 20]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 27|September 27]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 4|October 4]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 11|October 11]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 18|October 18]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 25|October 25]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#November 1|November 1]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#November 8|November 8]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#November 15|November 15]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#November 22| November 22]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#November 29|November 29]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#December 6|December 6]]<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#December 13|December 13]]<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
|}<br />
</center><br />
<br />
===September 13===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===September 20===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
<br />
===September 27===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===October 4===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><center></center><br />
<br />
===October 11===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
===October 18===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
<br />
===October 25===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===November 1===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===November 8===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===November 15===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
<br />
===November 22===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===November 29===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title:<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===December 6===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title:<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===December 13===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25097Graduate Algebraic Geometry Seminar Fall 20232023-08-31T15:58:56Z<p>Jcobb2: blank out talks</p>
<hr />
<div>'''When:''' 4:30-5:30 PM on Wednesday.<br />
<br />
'''Where:''' Van Vleck B119<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/XmdJ4hGbxvpbVVwr5 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 13|September 13]]<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 20|September 20]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#September 27|September 27]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 4|October 4]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 11|October 11]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 18|October 18]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#October 25|October 25]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#November 1|November 1]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#November 8|November 8]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#November 15|November 15]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#November 22| November 22]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#November 29|November 29]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#December 6|December 6]]<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#December 13|December 13]]<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" | <br />
|}<br />
</center><br />
<br />
===September 13===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===September 20===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | John Cobb<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Introduction to Intersection Theory<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: In this <s>advertisement</s> talk, I'd like to talk about some methods used in enumerative geometry. I'll define what a Chow ring is, count some things with it, and tell you why you should read "3264 and all that" this semester with me. <br />
|} <br />
</center><br />
<br />
===September 27===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | Yiyu Wang<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: An introduction to Macpherson's Chern classes<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: In this talk, I will start from a formula of the Euler characteristic number of a degree d smooth hypersurface in P^n and discuss how to generalize this formula to the singular case. This naturally leads to the notion of the Chern classes of a singular space. I will briefly introduce Macpherson's Chern classes which is a natural generalization of the ordinary Chern class and how to calculate these classes.<br />
|} <br />
</center><br />
<br />
===October 4===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Alex Hof<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Normal Cones in Algebraic Geometry<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: In this talk, we'll go over the definition of the normal cone of a closed subscheme, explore the geometric intuition behind it via a construction called the Rees algebra, and explain how it can be used to give geometric characterizations of apparently algebraic notions such as flatness and depth.<br />
|} <br />
</center><center></center><br />
<br />
===October 11===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Maya Banks<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Syzygies of Projective Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: The general slogan for the study of syzygies in geometry is that "geometric information about a projective variety is reflected in its sygygies." In this talk, we'll discuss some of the early results that kick-started this idea, such as Castelnuovo-Mumford regularity, quadric generation of varieties in P^n, and Green's Linear Syzygy Theorem. I'll go over all of the basic definitions and hopefully do lots of examples---in particular, this talk should be accessible to someone taking the intro Algebraic Geometry sequence.<br />
|} <br />
</center><br />
<br />
===October 18===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Asvin G<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
<br />
===October 25===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===November 1===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Kevin Dao<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Enriques-Kodaira Classification and its Influence on MMP<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: There is always more to say than there is time to say it. Let this abstract be an overly optimistic summary. I’ll tell you what the EK classification is, how it is achieved, the relevant development of birational algebraic geometry, and then point towards the difficulties in higher dimensions. I’ll also indicate, where possible and from what I know, the technical tools that are ubiquitous to the topic. If there is time, I will indicate a few problems and directions in either (a) the classification of (non-algebraic) surfaces, (b) rational curves on varieties, (c) major results of the MMP itself.<br />
|} <br />
</center><br />
<br />
===November 8===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Peter Yi Wei<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===November 15===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Dima Arinkin<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Hitchin Fibration<br />
<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
<br />
===November 22===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Yunfan He<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Variation of Hodge structure<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: I will review a little bit of the classic Hodge theory, and talk about how to generalize to the relative version.<br />
|} <br />
</center><br />
<br />
===November 29===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Jacob Wood<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title:<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===December 6===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Brian Hepler<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title:<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===December 13===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Sun Woo Park<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Introduction to Newton Polygon<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=25096Graduate Algebraic Geometry Seminar2023-08-31T15:47:29Z<p>Jcobb2: </p>
<hr />
<div>'''<br />
'''When? Where?:''' [https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2023 Link to current semester]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Current Organizers: ''' [https://johndcobb.github.io/ John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested, follow the link above to the current semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in three-dimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
==Ed Dewey's Wish List Of Olde==__NOTOC__<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
<br />
<br />
== Semesters ==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2023 Fall 2023]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2023&diff=25095Graduate Algebraic Geometry Seminar Fall 20232023-08-31T15:46:12Z<p>Jcobb2: initial commit</p>
<hr />
<div>'''When:''' 4:15-5:15 PM on Wednesday.<br />
<br />
'''Where:''' Van Vleck B119<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/XmdJ4hGbxvpbVVwr5 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#January 31|January 31]]<br />
| bgcolor="#C6D46E" | Mahrud Sayrafi<br />
| bgcolor="#BCE2FE" | Bounding the Multigraded Regularity of Powers of Ideals<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 1|February 1]]<br />
| bgcolor="#C6D46E" |John Cobb<br />
| bgcolor="#BCE2FE" |Introduction to Intersection Theory<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 8|February 8]]<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |An introduction to Macpherson's Chern classes<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 15|February 15]]<br />
| bgcolor="#C6D46E" |Alex Hof <br />
| bgcolor="#BCE2FE" |Normal Cones in Algebraic Geometry<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 22|February 22]]<br />
| bgcolor="#C6D46E" |Maya Banks<br />
| bgcolor="#BCE2FE" |Syzygies of Projective Varieties<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 3|March 1]]<br />
| bgcolor="#C6D46E" |Asvin G<br />
| bgcolor="#BCE2FE" |TBD<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 10|March 8]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 24|March 22]]<br />
| bgcolor="#C6D46E" |Kevin Dao<br />
| bgcolor="#BCE2FE" | Enriques-Kodaira Classification and its Influence on MMP<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 31|March 29]]<br />
| bgcolor="#C6D46E" |Peter Yi Wei<br />
| bgcolor="#BCE2FE" |TBD<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#April 7|April 5]]<br />
| bgcolor="#C6D46E" |Dima Arinkin<br />
| bgcolor="#BCE2FE" |Hitchin Fibration<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#April 14|April 12]]<br />
| bgcolor="#C6D46E" |Yunfan He<br />
| bgcolor="#BCE2FE" |Variation of Hodge structure<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#April 21|April 19]]<br />
| bgcolor="#C6D46E" | Jacob Wood<br />
| bgcolor="#BCE2FE" |K-Theory or something<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#April 28|April 26]]<br />
| bgcolor="#C6D46E" | Brian Hepler<br />
| bgcolor="#BCE2FE" |Condensed Sets<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#May 5|May 3]]<br />
| bgcolor="#C6D46E" | Sun Woo Park<br />
| bgcolor="#BCE2FE" |Introduction to Newton Polygon<br />
|}<br />
</center><br />
<br />
===January 31===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | Mahrud Sayrafi<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Bounding the Multigraded Regularity of Powers of Ideals<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: Building on a result of Swanson, Cutkosky-Herzog-Trung and Kodiyalam described the surprisingly predictable asymptotic behavior of Castelnuovo--Mumford regularity for powers of ideals on a projective space P^n: given an ideal I, there exist integers d and e such that for large enough n the regularity of I^n is exactly dn+e.<br />
Through a medley of examples we will see why asking the same question about an ideal I in the total coordinate ring S of a smooth projective toric variety X is interesting. After that I will summarize the ideas and methods we used to bound the region reg(I^n) as a subset of Pic(X) by proving that it contains a translate of reg(S) and is contained in a translate of Nef(X), with each bound translating by a fixed vector as n increases. Along the way will see some surprising behavior for multigraded regularity of modules. This is joint work with Juliette Bruce and Lauren Cranton Heller.<br />
|} <br />
</center><br />
<br />
===February 1===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | John Cobb<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Introduction to Intersection Theory<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: In this <s>advertisement</s> talk, I'd like to talk about some methods used in enumerative geometry. I'll define what a Chow ring is, count some things with it, and tell you why you should read "3264 and all that" this semester with me. <br />
|} <br />
</center><br />
<br />
===February 8===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | Yiyu Wang<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: An introduction to Macpherson's Chern classes<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: In this talk, I will start from a formula of the Euler characteristic number of a degree d smooth hypersurface in P^n and discuss how to generalize this formula to the singular case. This naturally leads to the notion of the Chern classes of a singular space. I will briefly introduce Macpherson's Chern classes which is a natural generalization of the ordinary Chern class and how to calculate these classes.<br />
|} <br />
</center><br />
<br />
===February 15===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Alex Hof<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Normal Cones in Algebraic Geometry<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: In this talk, we'll go over the definition of the normal cone of a closed subscheme, explore the geometric intuition behind it via a construction called the Rees algebra, and explain how it can be used to give geometric characterizations of apparently algebraic notions such as flatness and depth.<br />
|} <br />
</center><center></center><br />
<br />
===February 22===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Maya Banks<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Syzygies of Projective Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: The general slogan for the study of syzygies in geometry is that "geometric information about a projective variety is reflected in its sygygies." In this talk, we'll discuss some of the early results that kick-started this idea, such as Castelnuovo-Mumford regularity, quadric generation of varieties in P^n, and Green's Linear Syzygy Theorem. I'll go over all of the basic definitions and hopefully do lots of examples---in particular, this talk should be accessible to someone taking the intro Algebraic Geometry sequence.<br />
|} <br />
</center><br />
<br />
===March 1===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Asvin G<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
<br />
===March 8===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===March 22===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Kevin Dao<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Enriques-Kodaira Classification and its Influence on MMP<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: There is always more to say than there is time to say it. Let this abstract be an overly optimistic summary. I’ll tell you what the EK classification is, how it is achieved, the relevant development of birational algebraic geometry, and then point towards the difficulties in higher dimensions. I’ll also indicate, where possible and from what I know, the technical tools that are ubiquitous to the topic. If there is time, I will indicate a few problems and directions in either (a) the classification of (non-algebraic) surfaces, (b) rational curves on varieties, (c) major results of the MMP itself.<br />
|} <br />
</center><br />
<br />
===March 29===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Peter Yi Wei<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===April 5===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Dima Arinkin<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Hitchin Fibration<br />
<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
<br />
===April 12===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Yunfan He<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Variation of Hodge structure<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: I will review a little bit of the classic Hodge theory, and talk about how to generalize to the relative version.<br />
|} <br />
</center><br />
<br />
===April 19===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Jacob Wood<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title:<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===April 26===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Brian Hepler<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title:<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===May 3===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Sun Woo Park<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Introduction to Newton Polygon<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2023 Spring 2023]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program&diff=25071Directed Reading Program2023-08-23T19:14:09Z<p>Jcobb2: /* Past Semesters */</p>
<hr />
<div>'''When? Where?''' [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program_Fall_2023 Click here for a link to the current semester (Fall 2023).]<br />
<br />
'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic.<br />
<br />
=== How to apply ===<br />
Check out the [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program_Fall_2023 page for the Fall 2023 semester of DRP]. For project ideas, you may find it helpful to view the [[Directed Reading Program#Past Semesters | past semesters]].<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu[[File:Teams.jpg|frameless|450x450px]]<br />
<br />
== Past Semesters ==<br />
[https://wiki.math.wisc.edu/index.php/Directed_Reading_Program_Fall_2023 Fall 2023]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Directed_Reading_Program_Spring_2023 Spring 2023]<br />
<br />
[https://hilbert.math.wisc.edu/~drp/projects.html Click here for semesters before Spring 2023]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program&diff=25070Directed Reading Program2023-08-23T19:13:58Z<p>Jcobb2: </p>
<hr />
<div>'''When? Where?''' [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program_Fall_2023 Click here for a link to the current semester (Fall 2023).]<br />
<br />
'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic.<br />
<br />
=== How to apply ===<br />
Check out the [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program_Fall_2023 page for the Fall 2023 semester of DRP]. For project ideas, you may find it helpful to view the [[Directed Reading Program#Past Semesters | past semesters]].<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu[[File:Teams.jpg|frameless|450x450px]]<br />
<br />
== Past Semesters ==<br />
[https://wiki.math.wisc.edu/index.php/Directed_Reading_Program_Fall_2023 Fall 2023]<br />
[https://wiki.math.wisc.edu/index.php/Directed_Reading_Program_Spring_2023 Spring 2023]<br />
<br />
[https://hilbert.math.wisc.edu/~drp/projects.html Click here for semesters before Spring 2023]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Fall_2023&diff=25069Directed Reading Program Fall 20232023-08-23T19:10:56Z<p>Jcobb2: Initial Commit</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, December 6th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are closed.<br />
<br />
'''Mentors:''' Applications are open until Sunday, September 3rd. [https://forms.gle/47ezoixWrXxc5N8X8 Click here]<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
Coming soon...</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Spring_2023&diff=25068Directed Reading Program Spring 20232023-08-23T18:12:44Z<p>Jcobb2: </p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, April 26th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are closed.<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
{| class="wikitable"<br />
|+Spring 2023 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Probability and statistics<br />
|We will study the principles of Bayesian statistics. Topics may include conjugate priors, model selection, identifiability, mixture models. Emphasis will be placed on understanding Bayesian statistics as a method for unsupervised machine learning. Students with some background in computer programming will be able to work on problems related to Markov Chain Monte Carlo sampling. Well-prepared students will have the opportunity to contribute to a peer-reviewed academic journal article related to process control in semiconductor manufacturing. <br />
|Students should have some background in probability and/or statistics. Knowledge of some computer programming is preferred. This project should be one where a student can work independent, but the student can also expect to have regular contact and assistance from the mentor. <br />
|-<br />
|Stochastic Processes, Graph Theory, and Algebraic Topology<br />
|This DRP program is a continuation of an overview of graph neural networks from last semester. We will explore how incorporating homotopy theoretic invariants can help improve conventional graph neural networks, and explore various applications in medical sciences and social network analysis.<br />
|Students should have some background in probability and/or statistics. Knowledge of some computer programming is preferred. This project should be one where a student can work independent, but the student can also expect to have regular contact and assistance from the mentor. <br />
|-<br />
|Fractal geometry<br />
|In recent years, a surprising connection between two seemingly unrelated branches of math has emerged. Fractal dimension is a notion of size for sets which, unlike how we normally think about dimension, is not necessarily an integer (e.g. the rough shape of a coastline, the branching of a bolt of lightning, or the chaotic movement of a stock's price have non-integer dimension). Kolmogorov complexity, which measures how much information a string contains, can be applied to characterize some types of fractal dimension. This connection has already yielded impressive new results about fractal sets. <br />
In this DRP, we will start by understanding notions of fractal dimension and the definition/properties of Kolmogorov complexity. Then, we'll bridge the gap between the two via "effective" dimension. Effective dimension gives rise to elegant characterizations of both Hausdorff and packing dimension via the recently proven point-to-set principle, which we will study. Finally, we'll see some applications of this alternative definition, which makes it one of the most powerful new tools in fractal geometry. <br />
|Students should have completed at minimum 521 or comparable classes, but the more experience with proof-based math you have, the better. This material is very self-contained, but there are a number of definitions and challenging concepts. We'll go through everything at a reasonable pace, but some level of mathematical maturity will be helpful.<br />
|-<br />
|Number Theory<br />
|The primary source I plan to work through is P-adic Numbers by Fernando Q. Gouvêa. One goal of this project would be to understand the local-global principle, and to use Hasse-Minkowski's Theorem to classify rational solutions to various classical equations.<br />
|A semester of algebra. A semester of either analysis or topology will also be helpful but not strictly necassary in order to understand metric spaces<br />
|-<br />
|An introduction to matroids<br />
|A matroid is a mathematical object that generalizes the notion of linear independence in linear algebra. However, its applications are much broader, including graph theory and many problems in combinatorics. In this DRP, we will read Welsh's book Matroid Theory. The specific direction we take from there will be up to the students' interests.<br />
|No background is truly required, but some familiarity with graphs, linear algebra, basic set theory, etc would be useful.<br />
|-<br />
|Graph Theory<br />
|The goal of this DRP is to provide an introduction to hypergraph theory. There will be four main topics that we hope to cover:<br />
1. Basic Examples of Hypergraphs and Graph Coloring. <br />
2. Extremal Graph Theory (eg, Ramsey's Theorem, Hales-Jewett)<br />
3. The Probabilistic Method<br />
4. Linear Algebraic Methods<br />
We will only cover each topic on a surface level, but that is still sufficient to see some very strong and interesting results. <br />
|Some prior exposure to proofs is the only hard requirement. Some very basic notions in discrete probability and linear algebra will be used, but we can cover them if needed. A prior course in graph theory or discrete math might be helpful to better appreciate some of the generalizations through hypergraphs. <br />
|-<br />
|Set Theory / Logic<br />
|Let’s take an excursion into Set Theory! Set theory was originally developed as a way to formalize mathematical reasoning about infinite objects, but today it’s a full mathematical field with its own fascinating questions and results. We’ll certainly learn about ordinals and cardinals, and we’ll explore more topics depending on your interests and background!<br />
|Completed a 500-level math course. Preference for those who have taken Math 570 (Set Theory).<br />
|-<br />
|Algebra<br />
|In this project, we will use the methods of abstract algebra, and Cox Little and O'Shea's book "Ideals, Varieties and Algorithms," to generalize many of the topics we are familiar with when working with polynomials to multiple variables. We will also go beyond the text of this book and consider some unexpected approaches, as we learn about monomial orders, various types of ideals, and perhaps (optionally) some coding. Many types of mathematics will converge here.<br />
|Student should have completed a semester of algebra (541 or equivalent). Taking a second semester concurrently is a good idea, but not required.<br />
|-<br />
|Graph Neural Networks<br />
|Graph Neural Networks are a form of neural network that are designed to extract information from data in the form of a graph. The basic idea is that these are trainable networks that can learn from the various attributes of a graph (such as node-degree, number of edges, etc) and perform tasks at a node level (local) or graph level (global). It is an increasingly interesting area in machine learning and the aim of this DRP project will be to learn the basic theory of GNNs, implement some fundamental GNNs, and, time-permitting, come up with our own project for implementing a GNN to get something useful based on your interests. <br />
|Being comfortable with linear algebra, having any optimization experience, as well as some coding experience in python are important. You don't need much or any graph theory - we can cover the basics, which will be more than enough. Bonus if you've done some ML in the past. You'll be very independent for this project and be doing a lot of exploring with your group members.<br />
|}<br />
<br />
== Presentation Schedule ==<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:30-3:45 <br />
| bgcolor="#C6D46E" | Tianze Huang<br />
| bgcolor="#BCE2FE" | P-adic number and (maybe) hensels lemma<br />
|-<br />
| bgcolor="#E0E0E0" | 3:45-4:15<br />
| bgcolor="#C6D46E" | Jack Westbrook & Yixuan Hu<br />
| bgcolor="#BCE2FE" | Constructing Gödel’s Constructible Universe<br />
|-<br />
| bgcolor="#E0E0E0" | 4:15-4:30<br />
| bgcolor="#C6D46E" | S. Sudhir<br />
| bgcolor="#BCE2FE" | Inferring Tester Error Characteristics<br />
|-<br />
| bgcolor="#E0E0E0" | 4:30-4:45<br />
| bgcolor="#C6D46E" | A characterization of Hausdorff dimension via Komolgorov complexity<br />
| bgcolor="#BCE2FE" | Jack Maloney<br />
|-<br />
| bgcolor="#E0E0E0" |4:45-5:00<br />
| bgcolor="#C6D46E" |Jimmy Vineyard<br />
| bgcolor="#BCE2FE" | Community Detection with Line Graph Neural Networks<br />
|-<br />
| bgcolor="#E0E0E0" |5:00-5:30<br />
| bgcolor="#C6D46E" | Matt & PJ<br />
| bgcolor="#BCE2FE" | Matroid Presentation<br />
|-<br />
| bgcolor="#E0E0E0" | 5:30-5:45<br />
| bgcolor="#C6D46E" | Ruixuan Tu<br />
| bgcolor="#BCE2FE" | Representation power of GNN<br />
|}<br />
</center></div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Spring_2023&diff=24789Directed Reading Program Spring 20232023-04-18T21:52:56Z<p>Jcobb2: /* Presentation Schedule */</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, April 26th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are closed.<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
{| class="wikitable"<br />
|+Spring 2023 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Probability and statistics<br />
|We will study the principles of Bayesian statistics. Topics may include conjugate priors, model selection, identifiability, mixture models. Emphasis will be placed on understanding Bayesian statistics as a method for unsupervised machine learning. Students with some background in computer programming will be able to work on problems related to Markov Chain Monte Carlo sampling. Well-prepared students will have the opportunity to contribute to a peer-reviewed academic journal article related to process control in semiconductor manufacturing. <br />
|Students should have some background in probability and/or statistics. Knowledge of some computer programming is preferred. This project should be one where a student can work independent, but the student can also expect to have regular contact and assistance from the mentor. <br />
|-<br />
|Stochastic Processes, Graph Theory, and Algebraic Topology<br />
|This DRP program is a continuation of an overview of graph neural networks from last semester. We will explore how incorporating homotopy theoretic invariants can help improve conventional graph neural networks, and explore various applications in medical sciences and social network analysis.<br />
|Students should have some background in probability and/or statistics. Knowledge of some computer programming is preferred. This project should be one where a student can work independent, but the student can also expect to have regular contact and assistance from the mentor. <br />
|-<br />
|Fractal geometry<br />
|In recent years, a surprising connection between two seemingly unrelated branches of math has emerged. Fractal dimension is a notion of size for sets which, unlike how we normally think about dimension, is not necessarily an integer (e.g. the rough shape of a coastline, the branching of a bolt of lightning, or the chaotic movement of a stock's price have non-integer dimension). Kolmogorov complexity, which measures how much information a string contains, can be applied to characterize some types of fractal dimension. This connection has already yielded impressive new results about fractal sets. <br />
In this DRP, we will start by understanding notions of fractal dimension and the definition/properties of Kolmogorov complexity. Then, we'll bridge the gap between the two via "effective" dimension. Effective dimension gives rise to elegant characterizations of both Hausdorff and packing dimension via the recently proven point-to-set principle, which we will study. Finally, we'll see some applications of this alternative definition, which makes it one of the most powerful new tools in fractal geometry. <br />
|Students should have completed at minimum 521 or comparable classes, but the more experience with proof-based math you have, the better. This material is very self-contained, but there are a number of definitions and challenging concepts. We'll go through everything at a reasonable pace, but some level of mathematical maturity will be helpful.<br />
|-<br />
|Number Theory<br />
|The primary source I plan to work through is P-adic Numbers by Fernando Q. Gouvêa. One goal of this project would be to understand the local-global principle, and to use Hasse-Minkowski's Theorem to classify rational solutions to various classical equations.<br />
|A semester of algebra. A semester of either analysis or topology will also be helpful but not strictly necassary in order to understand metric spaces<br />
|-<br />
|An introduction to matroids<br />
|A matroid is a mathematical object that generalizes the notion of linear independence in linear algebra. However, its applications are much broader, including graph theory and many problems in combinatorics. In this DRP, we will read Welsh's book Matroid Theory. The specific direction we take from there will be up to the students' interests.<br />
|No background is truly required, but some familiarity with graphs, linear algebra, basic set theory, etc would be useful.<br />
|-<br />
|Graph Theory<br />
|The goal of this DRP is to provide an introduction to hypergraph theory. There will be four main topics that we hope to cover:<br />
1. Basic Examples of Hypergraphs and Graph Coloring. <br />
2. Extremal Graph Theory (eg, Ramsey's Theorem, Hales-Jewett)<br />
3. The Probabilistic Method<br />
4. Linear Algebraic Methods<br />
We will only cover each topic on a surface level, but that is still sufficient to see some very strong and interesting results. <br />
|Some prior exposure to proofs is the only hard requirement. Some very basic notions in discrete probability and linear algebra will be used, but we can cover them if needed. A prior course in graph theory or discrete math might be helpful to better appreciate some of the generalizations through hypergraphs. <br />
|-<br />
|Set Theory / Logic<br />
|Let’s take an excursion into Set Theory! Set theory was originally developed as a way to formalize mathematical reasoning about infinite objects, but today it’s a full mathematical field with its own fascinating questions and results. We’ll certainly learn about ordinals and cardinals, and we’ll explore more topics depending on your interests and background!<br />
|Completed a 500-level math course. Preference for those who have taken Math 570 (Set Theory).<br />
|-<br />
|Algebra<br />
|In this project, we will use the methods of abstract algebra, and Cox Little and O'Shea's book "Ideals, Varieties and Algorithms," to generalize many of the topics we are familiar with when working with polynomials to multiple variables. We will also go beyond the text of this book and consider some unexpected approaches, as we learn about monomial orders, various types of ideals, and perhaps (optionally) some coding. Many types of mathematics will converge here.<br />
|Student should have completed a semester of algebra (541 or equivalent). Taking a second semester concurrently is a good idea, but not required.<br />
|-<br />
|Graph Neural Networks<br />
|Graph Neural Networks are a form of neural network that are designed to extract information from data in the form of a graph. The basic idea is that these are trainable networks that can learn from the various attributes of a graph (such as node-degree, number of edges, etc) and perform tasks at a node level (local) or graph level (global). It is an increasingly interesting area in machine learning and the aim of this DRP project will be to learn the basic theory of GNNs, implement some fundamental GNNs, and, time-permitting, come up with our own project for implementing a GNN to get something useful based on your interests. <br />
|Being comfortable with linear algebra, having any optimization experience, as well as some coding experience in python are important. You don't need much or any graph theory - we can cover the basics, which will be more than enough. Bonus if you've done some ML in the past. You'll be very independent for this project and be doing a lot of exploring with your group members.<br />
|}<br />
<br />
== Presentation Schedule ==<br />
<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:30-3:45 ]<br />
| bgcolor="#C6D46E" | Tianze Huang<br />
| bgcolor="#BCE2FE" | P-adic number and (maybe) hensels lemma<br />
|-<br />
| bgcolor="#E0E0E0" | 3:45-4:15<br />
| bgcolor="#C6D46E" | Jack Westbrook & Yixuan Hu<br />
| bgcolor="#BCE2FE" | Constructing Gödel’s Constructible Universe<br />
|-<br />
| bgcolor="#E0E0E0" | 4:15-4:30<br />
| bgcolor="#C6D46E" | S. Sudhir<br />
| bgcolor="#BCE2FE" | Inferring Tester Error Characteristics<br />
|-<br />
| bgcolor="#E0E0E0" | 4:30-4:45<br />
| bgcolor="#C6D46E" | A characterization of Hausdorff dimension via Komolgorov complexity<br />
| bgcolor="#BCE2FE" | Jack Maloney<br />
|-<br />
| bgcolor="#E0E0E0" |4:45-5:00<br />
| bgcolor="#C6D46E" |Jimmy Vineyard<br />
| bgcolor="#BCE2FE" | Community Detection with Line Graph Neural Networks<br />
|-<br />
| bgcolor="#E0E0E0" |5:00-5:30<br />
| bgcolor="#C6D46E" | Matt & PJ<br />
| bgcolor="#BCE2FE" | Matroid Presentation<br />
|-<br />
| bgcolor="#E0E0E0" | 5:30-5:45<br />
| bgcolor="#C6D46E" | Ruixuan Tu<br />
| bgcolor="#BCE2FE" | Representation power of GNN<br />
|}<br />
</center></div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Spring_2023&diff=24788Directed Reading Program Spring 20232023-04-18T21:50:29Z<p>Jcobb2: Updaten schedule</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, April 26th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are closed.<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
{| class="wikitable"<br />
|+Spring 2023 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Probability and statistics<br />
|We will study the principles of Bayesian statistics. Topics may include conjugate priors, model selection, identifiability, mixture models. Emphasis will be placed on understanding Bayesian statistics as a method for unsupervised machine learning. Students with some background in computer programming will be able to work on problems related to Markov Chain Monte Carlo sampling. Well-prepared students will have the opportunity to contribute to a peer-reviewed academic journal article related to process control in semiconductor manufacturing. <br />
|Students should have some background in probability and/or statistics. Knowledge of some computer programming is preferred. This project should be one where a student can work independent, but the student can also expect to have regular contact and assistance from the mentor. <br />
|-<br />
|Stochastic Processes, Graph Theory, and Algebraic Topology<br />
|This DRP program is a continuation of an overview of graph neural networks from last semester. We will explore how incorporating homotopy theoretic invariants can help improve conventional graph neural networks, and explore various applications in medical sciences and social network analysis.<br />
|Students should have some background in probability and/or statistics. Knowledge of some computer programming is preferred. This project should be one where a student can work independent, but the student can also expect to have regular contact and assistance from the mentor. <br />
|-<br />
|Fractal geometry<br />
|In recent years, a surprising connection between two seemingly unrelated branches of math has emerged. Fractal dimension is a notion of size for sets which, unlike how we normally think about dimension, is not necessarily an integer (e.g. the rough shape of a coastline, the branching of a bolt of lightning, or the chaotic movement of a stock's price have non-integer dimension). Kolmogorov complexity, which measures how much information a string contains, can be applied to characterize some types of fractal dimension. This connection has already yielded impressive new results about fractal sets. <br />
In this DRP, we will start by understanding notions of fractal dimension and the definition/properties of Kolmogorov complexity. Then, we'll bridge the gap between the two via "effective" dimension. Effective dimension gives rise to elegant characterizations of both Hausdorff and packing dimension via the recently proven point-to-set principle, which we will study. Finally, we'll see some applications of this alternative definition, which makes it one of the most powerful new tools in fractal geometry. <br />
|Students should have completed at minimum 521 or comparable classes, but the more experience with proof-based math you have, the better. This material is very self-contained, but there are a number of definitions and challenging concepts. We'll go through everything at a reasonable pace, but some level of mathematical maturity will be helpful.<br />
|-<br />
|Number Theory<br />
|The primary source I plan to work through is P-adic Numbers by Fernando Q. Gouvêa. One goal of this project would be to understand the local-global principle, and to use Hasse-Minkowski's Theorem to classify rational solutions to various classical equations.<br />
|A semester of algebra. A semester of either analysis or topology will also be helpful but not strictly necassary in order to understand metric spaces<br />
|-<br />
|An introduction to matroids<br />
|A matroid is a mathematical object that generalizes the notion of linear independence in linear algebra. However, its applications are much broader, including graph theory and many problems in combinatorics. In this DRP, we will read Welsh's book Matroid Theory. The specific direction we take from there will be up to the students' interests.<br />
|No background is truly required, but some familiarity with graphs, linear algebra, basic set theory, etc would be useful.<br />
|-<br />
|Graph Theory<br />
|The goal of this DRP is to provide an introduction to hypergraph theory. There will be four main topics that we hope to cover:<br />
1. Basic Examples of Hypergraphs and Graph Coloring. <br />
2. Extremal Graph Theory (eg, Ramsey's Theorem, Hales-Jewett)<br />
3. The Probabilistic Method<br />
4. Linear Algebraic Methods<br />
We will only cover each topic on a surface level, but that is still sufficient to see some very strong and interesting results. <br />
|Some prior exposure to proofs is the only hard requirement. Some very basic notions in discrete probability and linear algebra will be used, but we can cover them if needed. A prior course in graph theory or discrete math might be helpful to better appreciate some of the generalizations through hypergraphs. <br />
|-<br />
|Set Theory / Logic<br />
|Let’s take an excursion into Set Theory! Set theory was originally developed as a way to formalize mathematical reasoning about infinite objects, but today it’s a full mathematical field with its own fascinating questions and results. We’ll certainly learn about ordinals and cardinals, and we’ll explore more topics depending on your interests and background!<br />
|Completed a 500-level math course. Preference for those who have taken Math 570 (Set Theory).<br />
|-<br />
|Algebra<br />
|In this project, we will use the methods of abstract algebra, and Cox Little and O'Shea's book "Ideals, Varieties and Algorithms," to generalize many of the topics we are familiar with when working with polynomials to multiple variables. We will also go beyond the text of this book and consider some unexpected approaches, as we learn about monomial orders, various types of ideals, and perhaps (optionally) some coding. Many types of mathematics will converge here.<br />
|Student should have completed a semester of algebra (541 or equivalent). Taking a second semester concurrently is a good idea, but not required.<br />
|-<br />
|Graph Neural Networks<br />
|Graph Neural Networks are a form of neural network that are designed to extract information from data in the form of a graph. The basic idea is that these are trainable networks that can learn from the various attributes of a graph (such as node-degree, number of edges, etc) and perform tasks at a node level (local) or graph level (global). It is an increasingly interesting area in machine learning and the aim of this DRP project will be to learn the basic theory of GNNs, implement some fundamental GNNs, and, time-permitting, come up with our own project for implementing a GNN to get something useful based on your interests. <br />
|Being comfortable with linear algebra, having any optimization experience, as well as some coding experience in python are important. You don't need much or any graph theory - we can cover the basics, which will be more than enough. Bonus if you've done some ML in the past. You'll be very independent for this project and be doing a lot of exploring with your group members.<br />
|}<br />
<br />
== Presentation Schedule ==<br />
<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:30-3:45 ]<br />
| bgcolor="#C6D46E" | Tianze Huang<br />
| bgcolor="#BCE2FE" | P-adic number and (maybe) hensels lemma<br />
|-<br />
| bgcolor="#E0E0E0" | 3:45-4:15<br />
| bgcolor="#C6D46E" | Jack Westbrook & Yixuan Hu<br />
| bgcolor="#BCE2FE" | Constructing Gödel’s Constructible Universe<br />
|-<br />
| bgcolor="#E0E0E0" | 4:15-4:30<br />
| bgcolor="#C6D46E" | S. Sudhir<br />
| bgcolor="#BCE2FE" | Inferring Tester Error Characteristics<br />
|-<br />
| bgcolor="#E0E0E0" | 4:30-4:45<br />
| bgcolor="#C6D46E" | Break<br />
| bgcolor="#BCE2FE" | N/A<br />
|-<br />
| bgcolor="#E0E0E0" |4:45-5:00<br />
| bgcolor="#C6D46E" |Jimmy Vineyard<br />
| bgcolor="#BCE2FE" | Community Detection with Line Graph Neural Networks<br />
|-<br />
| bgcolor="#E0E0E0" |5:00-5:30<br />
| bgcolor="#C6D46E" | Matt & PJ<br />
| bgcolor="#BCE2FE" | Matroid Presentation<br />
|-<br />
| bgcolor="#E0E0E0" | 5:30-5:45<br />
| bgcolor="#C6D46E" | Ruixuan Tu<br />
| bgcolor="#BCE2FE" | Representation power of GNN<br />
|}<br />
</center></div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Spring_2023&diff=24787Directed Reading Program Spring 20232023-04-17T21:46:24Z<p>Jcobb2: /* Presentation Schedule */</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, April 26th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are closed.<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
{| class="wikitable"<br />
|+Spring 2023 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Probability and statistics<br />
|We will study the principles of Bayesian statistics. Topics may include conjugate priors, model selection, identifiability, mixture models. Emphasis will be placed on understanding Bayesian statistics as a method for unsupervised machine learning. Students with some background in computer programming will be able to work on problems related to Markov Chain Monte Carlo sampling. Well-prepared students will have the opportunity to contribute to a peer-reviewed academic journal article related to process control in semiconductor manufacturing. <br />
|Students should have some background in probability and/or statistics. Knowledge of some computer programming is preferred. This project should be one where a student can work independent, but the student can also expect to have regular contact and assistance from the mentor. <br />
|-<br />
|Stochastic Processes, Graph Theory, and Algebraic Topology<br />
|This DRP program is a continuation of an overview of graph neural networks from last semester. We will explore how incorporating homotopy theoretic invariants can help improve conventional graph neural networks, and explore various applications in medical sciences and social network analysis.<br />
|Students should have some background in probability and/or statistics. Knowledge of some computer programming is preferred. This project should be one where a student can work independent, but the student can also expect to have regular contact and assistance from the mentor. <br />
|-<br />
|Fractal geometry<br />
|In recent years, a surprising connection between two seemingly unrelated branches of math has emerged. Fractal dimension is a notion of size for sets which, unlike how we normally think about dimension, is not necessarily an integer (e.g. the rough shape of a coastline, the branching of a bolt of lightning, or the chaotic movement of a stock's price have non-integer dimension). Kolmogorov complexity, which measures how much information a string contains, can be applied to characterize some types of fractal dimension. This connection has already yielded impressive new results about fractal sets. <br />
In this DRP, we will start by understanding notions of fractal dimension and the definition/properties of Kolmogorov complexity. Then, we'll bridge the gap between the two via "effective" dimension. Effective dimension gives rise to elegant characterizations of both Hausdorff and packing dimension via the recently proven point-to-set principle, which we will study. Finally, we'll see some applications of this alternative definition, which makes it one of the most powerful new tools in fractal geometry. <br />
|Students should have completed at minimum 521 or comparable classes, but the more experience with proof-based math you have, the better. This material is very self-contained, but there are a number of definitions and challenging concepts. We'll go through everything at a reasonable pace, but some level of mathematical maturity will be helpful.<br />
|-<br />
|Number Theory<br />
|The primary source I plan to work through is P-adic Numbers by Fernando Q. Gouvêa. One goal of this project would be to understand the local-global principle, and to use Hasse-Minkowski's Theorem to classify rational solutions to various classical equations.<br />
|A semester of algebra. A semester of either analysis or topology will also be helpful but not strictly necassary in order to understand metric spaces<br />
|-<br />
|An introduction to matroids<br />
|A matroid is a mathematical object that generalizes the notion of linear independence in linear algebra. However, its applications are much broader, including graph theory and many problems in combinatorics. In this DRP, we will read Welsh's book Matroid Theory. The specific direction we take from there will be up to the students' interests.<br />
|No background is truly required, but some familiarity with graphs, linear algebra, basic set theory, etc would be useful.<br />
|-<br />
|Graph Theory<br />
|The goal of this DRP is to provide an introduction to hypergraph theory. There will be four main topics that we hope to cover:<br />
1. Basic Examples of Hypergraphs and Graph Coloring. <br />
2. Extremal Graph Theory (eg, Ramsey's Theorem, Hales-Jewett)<br />
3. The Probabilistic Method<br />
4. Linear Algebraic Methods<br />
We will only cover each topic on a surface level, but that is still sufficient to see some very strong and interesting results. <br />
|Some prior exposure to proofs is the only hard requirement. Some very basic notions in discrete probability and linear algebra will be used, but we can cover them if needed. A prior course in graph theory or discrete math might be helpful to better appreciate some of the generalizations through hypergraphs. <br />
|-<br />
|Set Theory / Logic<br />
|Let’s take an excursion into Set Theory! Set theory was originally developed as a way to formalize mathematical reasoning about infinite objects, but today it’s a full mathematical field with its own fascinating questions and results. We’ll certainly learn about ordinals and cardinals, and we’ll explore more topics depending on your interests and background!<br />
|Completed a 500-level math course. Preference for those who have taken Math 570 (Set Theory).<br />
|-<br />
|Algebra<br />
|In this project, we will use the methods of abstract algebra, and Cox Little and O'Shea's book "Ideals, Varieties and Algorithms," to generalize many of the topics we are familiar with when working with polynomials to multiple variables. We will also go beyond the text of this book and consider some unexpected approaches, as we learn about monomial orders, various types of ideals, and perhaps (optionally) some coding. Many types of mathematics will converge here.<br />
|Student should have completed a semester of algebra (541 or equivalent). Taking a second semester concurrently is a good idea, but not required.<br />
|-<br />
|Graph Neural Networks<br />
|Graph Neural Networks are a form of neural network that are designed to extract information from data in the form of a graph. The basic idea is that these are trainable networks that can learn from the various attributes of a graph (such as node-degree, number of edges, etc) and perform tasks at a node level (local) or graph level (global). It is an increasingly interesting area in machine learning and the aim of this DRP project will be to learn the basic theory of GNNs, implement some fundamental GNNs, and, time-permitting, come up with our own project for implementing a GNN to get something useful based on your interests. <br />
|Being comfortable with linear algebra, having any optimization experience, as well as some coding experience in python are important. You don't need much or any graph theory - we can cover the basics, which will be more than enough. Bonus if you've done some ML in the past. You'll be very independent for this project and be doing a lot of exploring with your group members.<br />
|}<br />
<br />
== Presentation Schedule ==<br />
<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:45-4:00 ]<br />
| bgcolor="#C6D46E" | Tianze Huang<br />
| bgcolor="#BCE2FE" | P-adic number and (maybe) hensels lemma<br />
|-<br />
| bgcolor="#E0E0E0" | 4:00-4:30<br />
| bgcolor="#C6D46E" | Jack Westbrook & Yixuan Hu<br />
| bgcolor="#BCE2FE" | Constructing Gödel’s Constructible Universe<br />
|-<br />
| bgcolor="#E0E0E0" | 4:30-4:45<br />
| bgcolor="#C6D46E" | S. Sudhir<br />
| bgcolor="#BCE2FE" | Inferring Testor Error Characteristics<br />
|-<br />
| bgcolor="#E0E0E0" |4:45-5:00<br />
| bgcolor="#C6D46E" |Jimmy Vineyard<br />
| bgcolor="#BCE2FE" | Community Detection with Line Graph Neural Networks<br />
|-<br />
| bgcolor="#E0E0E0" |5:00-5:30<br />
| bgcolor="#C6D46E" | Matt & PJ<br />
| bgcolor="#BCE2FE" | Matroid Presentation<br />
|-<br />
| bgcolor="#E0E0E0" | 5:30-5:45<br />
| bgcolor="#C6D46E" | Ruixuan Tu<br />
| bgcolor="#BCE2FE" | Representation power of GNN<br />
|}<br />
</center></div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Directed_Reading_Program_Spring_2023&diff=24786Directed Reading Program Spring 20232023-04-17T21:46:14Z<p>Jcobb2: /* Presentation Schedule */</p>
<hr />
<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
<br />
'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
<br />
'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, John Cobb, John Spoerl, Karan Srivastava<br />
<br />
===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, April 26th.'''<br />
<br />
=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
<br />
'''Students:''' Applications are closed.<br />
<br />
'''Mentors:''' Applications are closed.<br />
<br />
===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
<br />
== Projects ==<br />
{| class="wikitable"<br />
|+Spring 2023 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Probability and statistics<br />
|We will study the principles of Bayesian statistics. Topics may include conjugate priors, model selection, identifiability, mixture models. Emphasis will be placed on understanding Bayesian statistics as a method for unsupervised machine learning. Students with some background in computer programming will be able to work on problems related to Markov Chain Monte Carlo sampling. Well-prepared students will have the opportunity to contribute to a peer-reviewed academic journal article related to process control in semiconductor manufacturing. <br />
|Students should have some background in probability and/or statistics. Knowledge of some computer programming is preferred. This project should be one where a student can work independent, but the student can also expect to have regular contact and assistance from the mentor. <br />
|-<br />
|Stochastic Processes, Graph Theory, and Algebraic Topology<br />
|This DRP program is a continuation of an overview of graph neural networks from last semester. We will explore how incorporating homotopy theoretic invariants can help improve conventional graph neural networks, and explore various applications in medical sciences and social network analysis.<br />
|Students should have some background in probability and/or statistics. Knowledge of some computer programming is preferred. This project should be one where a student can work independent, but the student can also expect to have regular contact and assistance from the mentor. <br />
|-<br />
|Fractal geometry<br />
|In recent years, a surprising connection between two seemingly unrelated branches of math has emerged. Fractal dimension is a notion of size for sets which, unlike how we normally think about dimension, is not necessarily an integer (e.g. the rough shape of a coastline, the branching of a bolt of lightning, or the chaotic movement of a stock's price have non-integer dimension). Kolmogorov complexity, which measures how much information a string contains, can be applied to characterize some types of fractal dimension. This connection has already yielded impressive new results about fractal sets. <br />
In this DRP, we will start by understanding notions of fractal dimension and the definition/properties of Kolmogorov complexity. Then, we'll bridge the gap between the two via "effective" dimension. Effective dimension gives rise to elegant characterizations of both Hausdorff and packing dimension via the recently proven point-to-set principle, which we will study. Finally, we'll see some applications of this alternative definition, which makes it one of the most powerful new tools in fractal geometry. <br />
|Students should have completed at minimum 521 or comparable classes, but the more experience with proof-based math you have, the better. This material is very self-contained, but there are a number of definitions and challenging concepts. We'll go through everything at a reasonable pace, but some level of mathematical maturity will be helpful.<br />
|-<br />
|Number Theory<br />
|The primary source I plan to work through is P-adic Numbers by Fernando Q. Gouvêa. One goal of this project would be to understand the local-global principle, and to use Hasse-Minkowski's Theorem to classify rational solutions to various classical equations.<br />
|A semester of algebra. A semester of either analysis or topology will also be helpful but not strictly necassary in order to understand metric spaces<br />
|-<br />
|An introduction to matroids<br />
|A matroid is a mathematical object that generalizes the notion of linear independence in linear algebra. However, its applications are much broader, including graph theory and many problems in combinatorics. In this DRP, we will read Welsh's book Matroid Theory. The specific direction we take from there will be up to the students' interests.<br />
|No background is truly required, but some familiarity with graphs, linear algebra, basic set theory, etc would be useful.<br />
|-<br />
|Graph Theory<br />
|The goal of this DRP is to provide an introduction to hypergraph theory. There will be four main topics that we hope to cover:<br />
1. Basic Examples of Hypergraphs and Graph Coloring. <br />
2. Extremal Graph Theory (eg, Ramsey's Theorem, Hales-Jewett)<br />
3. The Probabilistic Method<br />
4. Linear Algebraic Methods<br />
We will only cover each topic on a surface level, but that is still sufficient to see some very strong and interesting results. <br />
|Some prior exposure to proofs is the only hard requirement. Some very basic notions in discrete probability and linear algebra will be used, but we can cover them if needed. A prior course in graph theory or discrete math might be helpful to better appreciate some of the generalizations through hypergraphs. <br />
|-<br />
|Set Theory / Logic<br />
|Let’s take an excursion into Set Theory! Set theory was originally developed as a way to formalize mathematical reasoning about infinite objects, but today it’s a full mathematical field with its own fascinating questions and results. We’ll certainly learn about ordinals and cardinals, and we’ll explore more topics depending on your interests and background!<br />
|Completed a 500-level math course. Preference for those who have taken Math 570 (Set Theory).<br />
|-<br />
|Algebra<br />
|In this project, we will use the methods of abstract algebra, and Cox Little and O'Shea's book "Ideals, Varieties and Algorithms," to generalize many of the topics we are familiar with when working with polynomials to multiple variables. We will also go beyond the text of this book and consider some unexpected approaches, as we learn about monomial orders, various types of ideals, and perhaps (optionally) some coding. Many types of mathematics will converge here.<br />
|Student should have completed a semester of algebra (541 or equivalent). Taking a second semester concurrently is a good idea, but not required.<br />
|-<br />
|Graph Neural Networks<br />
|Graph Neural Networks are a form of neural network that are designed to extract information from data in the form of a graph. The basic idea is that these are trainable networks that can learn from the various attributes of a graph (such as node-degree, number of edges, etc) and perform tasks at a node level (local) or graph level (global). It is an increasingly interesting area in machine learning and the aim of this DRP project will be to learn the basic theory of GNNs, implement some fundamental GNNs, and, time-permitting, come up with our own project for implementing a GNN to get something useful based on your interests. <br />
|Being comfortable with linear algebra, having any optimization experience, as well as some coding experience in python are important. You don't need much or any graph theory - we can cover the basics, which will be more than enough. Bonus if you've done some ML in the past. You'll be very independent for this project and be doing a lot of exploring with your group members.<br />
|}<br />
<br />
== Presentation Schedule ==<br />
<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Time'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speakers'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" | 3:45-4:00 ]<br />
| bgcolor="#C6D46E" | Tianze Huang<br />
| bgcolor="#BCE2FE" | P-adic number and (maybe) hensels lemma<br />
|-<br />
| bgcolor="#E0E0E0" | 4:00-4:30<br />
| bgcolor="#C6D46E" | Jack Westbrook & Yixuan Hu<br />
| bgcolor="#BCE2FE" | Constructing Gödel’s Constructible Universe<br />
|-<br />
| bgcolor="#E0E0E0" | 4:30-4:45<br />
| bgcolor="#C6D46E" | S. Sudhir<br />
| bgcolor="#BCE2FE" | Inferring Testor Error Characteristics<br />
|-<br />
| bgcolor="#E0E0E0" |4:45-5:00<br />
| bgcolor="#C6D46E" |Jimmy Vineyard<br />
| bgcolor="#BCE2FE" | Community Detection with Line Graph Neural Networks<br />
|-<br />
| bgcolor="#E0E0E0" |5:00-5:30<br />
| bgcolor="#C6D46E" | Matt & PJ<br />
| bgcolor="#BCE2FE" | Matroid Presentation<br />
<br />
| bgcolor="#E0E0E0" | 5:30-5:45<br />
| bgcolor="#C6D46E" | Ruixuan Tu<br />
| bgcolor="#BCE2FE" | Representation power of GNN<br />
|}<br />
</center></div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2023&diff=24775Graduate Algebraic Geometry Seminar Spring 20232023-04-12T21:09:12Z<p>Jcobb2: /* April 12 */</p>
<hr />
<div>'''When:''' 4:15-5:15 PM on Wednesday.<br />
<br />
'''Where:''' Van Vleck B119<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/XmdJ4hGbxvpbVVwr5 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#January 31|January 31]]<br />
| bgcolor="#C6D46E" | Mahrud Sayrafi<br />
| bgcolor="#BCE2FE" | Bounding the Multigraded Regularity of Powers of Ideals<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 1|February 1]]<br />
| bgcolor="#C6D46E" |John Cobb<br />
| bgcolor="#BCE2FE" |Introduction to Intersection Theory<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 8|February 8]]<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |An introduction to Macpherson's Chern classes<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 15|February 15]]<br />
| bgcolor="#C6D46E" |Alex Hof <br />
| bgcolor="#BCE2FE" |Normal Cones in Algebraic Geometry<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 22|February 22]]<br />
| bgcolor="#C6D46E" |Maya Banks<br />
| bgcolor="#BCE2FE" |Syzygies of Projective Varieties<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 3|March 1]]<br />
| bgcolor="#C6D46E" |Asvin G<br />
| bgcolor="#BCE2FE" |TBD<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 10|March 8]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 24|March 22]]<br />
| bgcolor="#C6D46E" |Kevin Dao<br />
| bgcolor="#BCE2FE" | Enriques-Kodaira Classification and its Influence on MMP<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 31|March 29]]<br />
| bgcolor="#C6D46E" |Peter Yi Wei<br />
| bgcolor="#BCE2FE" |TBD<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#April 7|April 5]]<br />
| bgcolor="#C6D46E" |Dima Arinkin<br />
| bgcolor="#BCE2FE" |Hitchin Fibration<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#April 14|April 12]]<br />
| bgcolor="#C6D46E" |Yunfan He<br />
| bgcolor="#BCE2FE" |Variation of Hodge structure<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#April 21|April 19]]<br />
| bgcolor="#C6D46E" | Jacob Wood<br />
| bgcolor="#BCE2FE" |K-Theory or something<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#April 28|April 26]]<br />
| bgcolor="#C6D46E" | Brian Hepler<br />
| bgcolor="#BCE2FE" |Condensed Sets<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#May 5|May 3]]<br />
| bgcolor="#C6D46E" | Sun Woo Park<br />
| bgcolor="#BCE2FE" |Introduction to Newton Polygon<br />
|}<br />
</center><br />
<br />
===January 31===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | Mahrud Sayrafi<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Bounding the Multigraded Regularity of Powers of Ideals<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: Building on a result of Swanson, Cutkosky-Herzog-Trung and Kodiyalam described the surprisingly predictable asymptotic behavior of Castelnuovo--Mumford regularity for powers of ideals on a projective space P^n: given an ideal I, there exist integers d and e such that for large enough n the regularity of I^n is exactly dn+e.<br />
Through a medley of examples we will see why asking the same question about an ideal I in the total coordinate ring S of a smooth projective toric variety X is interesting. After that I will summarize the ideas and methods we used to bound the region reg(I^n) as a subset of Pic(X) by proving that it contains a translate of reg(S) and is contained in a translate of Nef(X), with each bound translating by a fixed vector as n increases. Along the way will see some surprising behavior for multigraded regularity of modules. This is joint work with Juliette Bruce and Lauren Cranton Heller.<br />
|} <br />
</center><br />
<br />
===February 1===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | John Cobb<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Introduction to Intersection Theory<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: In this <s>advertisement</s> talk, I'd like to talk about some methods used in enumerative geometry. I'll define what a Chow ring is, count some things with it, and tell you why you should read "3264 and all that" this semester with me. <br />
|} <br />
</center><br />
<br />
===February 8===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | Yiyu Wang<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: An introduction to Macpherson's Chern classes<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: In this talk, I will start from a formula of the Euler characteristic number of a degree d smooth hypersurface in P^n and discuss how to generalize this formula to the singular case. This naturally leads to the notion of the Chern classes of a singular space. I will briefly introduce Macpherson's Chern classes which is a natural generalization of the ordinary Chern class and how to calculate these classes.<br />
|} <br />
</center><br />
<br />
===February 15===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Alex Hof<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Normal Cones in Algebraic Geometry<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: In this talk, we'll go over the definition of the normal cone of a closed subscheme, explore the geometric intuition behind it via a construction called the Rees algebra, and explain how it can be used to give geometric characterizations of apparently algebraic notions such as flatness and depth.<br />
|} <br />
</center><center></center><br />
<br />
===February 22===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Maya Banks<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Syzygies of Projective Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: The general slogan for the study of syzygies in geometry is that "geometric information about a projective variety is reflected in its sygygies." In this talk, we'll discuss some of the early results that kick-started this idea, such as Castelnuovo-Mumford regularity, quadric generation of varieties in P^n, and Green's Linear Syzygy Theorem. I'll go over all of the basic definitions and hopefully do lots of examples---in particular, this talk should be accessible to someone taking the intro Algebraic Geometry sequence.<br />
|} <br />
</center><br />
<br />
===March 1===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Asvin G<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
<br />
===March 8===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===March 22===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Kevin Dao<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Enriques-Kodaira Classification and its Influence on MMP<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: There is always more to say than there is time to say it. Let this abstract be an overly optimistic summary. I’ll tell you what the EK classification is, how it is achieved, the relevant development of birational algebraic geometry, and then point towards the difficulties in higher dimensions. I’ll also indicate, where possible and from what I know, the technical tools that are ubiquitous to the topic. If there is time, I will indicate a few problems and directions in either (a) the classification of (non-algebraic) surfaces, (b) rational curves on varieties, (c) major results of the MMP itself.<br />
|} <br />
</center><br />
<br />
===March 29===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Peter Yi Wei<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===April 5===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Dima Arinkin<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Hitchin Fibration<br />
<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
<br />
===April 12===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Yunfan He<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Variation of Hodge structure<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: I will review a little bit of the classic Hodge theory, and talk about how to generalize to the relative version.<br />
|} <br />
</center><br />
<br />
===April 19===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Jacob Wood<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title:<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===April 26===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Brian Hepler<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title:<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===May 3===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Sun Woo Park<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Introduction to Newton Polygon<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2023&diff=24759Graduate Algebraic Geometry Seminar Spring 20232023-04-10T15:56:28Z<p>Jcobb2: /* Talks */</p>
<hr />
<div>'''When:''' 4:15-5:15 PM on Wednesday.<br />
<br />
'''Where:''' Van Vleck B119<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/XmdJ4hGbxvpbVVwr5 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#January 31|January 31]]<br />
| bgcolor="#C6D46E" | Mahrud Sayrafi<br />
| bgcolor="#BCE2FE" | Bounding the Multigraded Regularity of Powers of Ideals<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 1|February 1]]<br />
| bgcolor="#C6D46E" |John Cobb<br />
| bgcolor="#BCE2FE" |Introduction to Intersection Theory<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 8|February 8]]<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |An introduction to Macpherson's Chern classes<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 15|February 15]]<br />
| bgcolor="#C6D46E" |Alex Hof <br />
| bgcolor="#BCE2FE" |Normal Cones in Algebraic Geometry<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 22|February 22]]<br />
| bgcolor="#C6D46E" |Maya Banks<br />
| bgcolor="#BCE2FE" |Syzygies of Projective Varieties<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 3|March 1]]<br />
| bgcolor="#C6D46E" |Asvin G<br />
| bgcolor="#BCE2FE" |TBD<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 10|March 8]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 24|March 22]]<br />
| bgcolor="#C6D46E" |Kevin Dao<br />
| bgcolor="#BCE2FE" | Enriques-Kodaira Classification and its Influence on MMP<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 31|March 29]]<br />
| bgcolor="#C6D46E" |Peter Yi Wei<br />
| bgcolor="#BCE2FE" |TBD<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#April 7|April 5]]<br />
| bgcolor="#C6D46E" |Dima Arinkin<br />
| bgcolor="#BCE2FE" |Hitchin Fibration<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#April 14|April 12]]<br />
| bgcolor="#C6D46E" |Yunfan He<br />
| bgcolor="#BCE2FE" |Variation of Hodge structure<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#April 21|April 19]]<br />
| bgcolor="#C6D46E" | Jacob Wood<br />
| bgcolor="#BCE2FE" |K-Theory or something<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#April 28|April 26]]<br />
| bgcolor="#C6D46E" | Brian Hepler<br />
| bgcolor="#BCE2FE" |Condensed Sets<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#May 5|May 3]]<br />
| bgcolor="#C6D46E" | Sun Woo Park<br />
| bgcolor="#BCE2FE" |Introduction to Newton Polygon<br />
|}<br />
</center><br />
<br />
===January 31===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | Mahrud Sayrafi<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Bounding the Multigraded Regularity of Powers of Ideals<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: Building on a result of Swanson, Cutkosky-Herzog-Trung and Kodiyalam described the surprisingly predictable asymptotic behavior of Castelnuovo--Mumford regularity for powers of ideals on a projective space P^n: given an ideal I, there exist integers d and e such that for large enough n the regularity of I^n is exactly dn+e.<br />
Through a medley of examples we will see why asking the same question about an ideal I in the total coordinate ring S of a smooth projective toric variety X is interesting. After that I will summarize the ideas and methods we used to bound the region reg(I^n) as a subset of Pic(X) by proving that it contains a translate of reg(S) and is contained in a translate of Nef(X), with each bound translating by a fixed vector as n increases. Along the way will see some surprising behavior for multigraded regularity of modules. This is joint work with Juliette Bruce and Lauren Cranton Heller.<br />
|} <br />
</center><br />
<br />
===February 1===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | John Cobb<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Introduction to Intersection Theory<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: In this <s>advertisement</s> talk, I'd like to talk about some methods used in enumerative geometry. I'll define what a Chow ring is, count some things with it, and tell you why you should read "3264 and all that" this semester with me. <br />
|} <br />
</center><br />
<br />
===February 8===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | Yiyu Wang<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: An introduction to Macpherson's Chern classes<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: In this talk, I will start from a formula of the Euler characteristic number of a degree d smooth hypersurface in P^n and discuss how to generalize this formula to the singular case. This naturally leads to the notion of the Chern classes of a singular space. I will briefly introduce Macpherson's Chern classes which is a natural generalization of the ordinary Chern class and how to calculate these classes.<br />
|} <br />
</center><br />
<br />
===February 15===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Alex Hof<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Normal Cones in Algebraic Geometry<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: In this talk, we'll go over the definition of the normal cone of a closed subscheme, explore the geometric intuition behind it via a construction called the Rees algebra, and explain how it can be used to give geometric characterizations of apparently algebraic notions such as flatness and depth.<br />
|} <br />
</center><center></center><br />
<br />
===February 22===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Maya Banks<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Syzygies of Projective Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: The general slogan for the study of syzygies in geometry is that "geometric information about a projective variety is reflected in its sygygies." In this talk, we'll discuss some of the early results that kick-started this idea, such as Castelnuovo-Mumford regularity, quadric generation of varieties in P^n, and Green's Linear Syzygy Theorem. I'll go over all of the basic definitions and hopefully do lots of examples---in particular, this talk should be accessible to someone taking the intro Algebraic Geometry sequence.<br />
|} <br />
</center><br />
<br />
===March 1===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Asvin G<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
<br />
===March 8===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===March 22===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Kevin Dao<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Enriques-Kodaira Classification and its Influence on MMP<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: There is always more to say than there is time to say it. Let this abstract be an overly optimistic summary. I’ll tell you what the EK classification is, how it is achieved, the relevant development of birational algebraic geometry, and then point towards the difficulties in higher dimensions. I’ll also indicate, where possible and from what I know, the technical tools that are ubiquitous to the topic. If there is time, I will indicate a few problems and directions in either (a) the classification of (non-algebraic) surfaces, (b) rational curves on varieties, (c) major results of the MMP itself.<br />
|} <br />
</center><br />
<br />
===March 29===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Peter Yi Wei<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===April 5===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Dima Arinkin<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Hitchin Fibration<br />
<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
<br />
===April 12===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Yunfan He<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Introduction to the Deligne-Illusie theory<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: I will review a little bit of the classic Hodge theory, and talk about how to generalize to the relative version.<br />
|} <br />
</center><br />
<br />
===April 19===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Jacob Wood<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title:<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===April 26===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Brian Hepler<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title:<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===May 3===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Sun Woo Park<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Introduction to Newton Polygon<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2023&diff=24720Graduate Algebraic Geometry Seminar Spring 20232023-03-30T16:45:01Z<p>Jcobb2: /* Talks */</p>
<hr />
<div>'''When:''' 4:15-5:15 PM on Wednesday.<br />
<br />
'''Where:''' Van Vleck B119<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/XmdJ4hGbxvpbVVwr5 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#January 31|January 31]]<br />
| bgcolor="#C6D46E" | Mahrud Sayrafi<br />
| bgcolor="#BCE2FE" | Bounding the Multigraded Regularity of Powers of Ideals<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 1|February 1]]<br />
| bgcolor="#C6D46E" |John Cobb<br />
| bgcolor="#BCE2FE" |Introduction to Intersection Theory<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 8|February 8]]<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |An introduction to Macpherson's Chern classes<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 15|February 15]]<br />
| bgcolor="#C6D46E" |Alex Hof <br />
| bgcolor="#BCE2FE" |Normal Cones in Algebraic Geometry<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 22|February 22]]<br />
| bgcolor="#C6D46E" |Maya Banks<br />
| bgcolor="#BCE2FE" |Syzygies of Projective Varieties<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 3|March 1]]<br />
| bgcolor="#C6D46E" |Asvin G<br />
| bgcolor="#BCE2FE" |TBD<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 10|March 8]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 24|March 22]]<br />
| bgcolor="#C6D46E" |Kevin Dao<br />
| bgcolor="#BCE2FE" | Enriques-Kodaira Classification and its Influence on MMP<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 31|March 29]]<br />
| bgcolor="#C6D46E" |Peter Yi Wei<br />
| bgcolor="#BCE2FE" |TBD<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#April 7|April 5]]<br />
| bgcolor="#C6D46E" |Dima Arinkin<br />
| bgcolor="#BCE2FE" |Hitchin Fibration<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#April 14|April 12]]<br />
| bgcolor="#C6D46E" |Yunfan He<br />
| bgcolor="#BCE2FE" |Introduction to the Deligne-Illusie theory<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#April 21|April 19]]<br />
| bgcolor="#C6D46E" | Jacob Wood<br />
| bgcolor="#BCE2FE" |K-Theory or something<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#April 28|April 26]]<br />
| bgcolor="#C6D46E" | Brian Hepler<br />
| bgcolor="#BCE2FE" |Condensed Sets<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#May 5|May 3]]<br />
| bgcolor="#C6D46E" | Sun Woo Park<br />
| bgcolor="#BCE2FE" |Introduction to Newton Polygon<br />
|}<br />
</center><br />
<br />
===January 31===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | Mahrud Sayrafi<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Bounding the Multigraded Regularity of Powers of Ideals<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: Building on a result of Swanson, Cutkosky-Herzog-Trung and Kodiyalam described the surprisingly predictable asymptotic behavior of Castelnuovo--Mumford regularity for powers of ideals on a projective space P^n: given an ideal I, there exist integers d and e such that for large enough n the regularity of I^n is exactly dn+e.<br />
Through a medley of examples we will see why asking the same question about an ideal I in the total coordinate ring S of a smooth projective toric variety X is interesting. After that I will summarize the ideas and methods we used to bound the region reg(I^n) as a subset of Pic(X) by proving that it contains a translate of reg(S) and is contained in a translate of Nef(X), with each bound translating by a fixed vector as n increases. Along the way will see some surprising behavior for multigraded regularity of modules. This is joint work with Juliette Bruce and Lauren Cranton Heller.<br />
|} <br />
</center><br />
<br />
===February 1===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | John Cobb<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Introduction to Intersection Theory<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: In this <s>advertisement</s> talk, I'd like to talk about some methods used in enumerative geometry. I'll define what a Chow ring is, count some things with it, and tell you why you should read "3264 and all that" this semester with me. <br />
|} <br />
</center><br />
<br />
===February 8===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | Yiyu Wang<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: An introduction to Macpherson's Chern classes<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: In this talk, I will start from a formula of the Euler characteristic number of a degree d smooth hypersurface in P^n and discuss how to generalize this formula to the singular case. This naturally leads to the notion of the Chern classes of a singular space. I will briefly introduce Macpherson's Chern classes which is a natural generalization of the ordinary Chern class and how to calculate these classes.<br />
|} <br />
</center><br />
<br />
===February 15===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Alex Hof<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Normal Cones in Algebraic Geometry<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: In this talk, we'll go over the definition of the normal cone of a closed subscheme, explore the geometric intuition behind it via a construction called the Rees algebra, and explain how it can be used to give geometric characterizations of apparently algebraic notions such as flatness and depth.<br />
|} <br />
</center><center></center><br />
<br />
===February 22===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Maya Banks<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Syzygies of Projective Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: The general slogan for the study of syzygies in geometry is that "geometric information about a projective variety is reflected in its sygygies." In this talk, we'll discuss some of the early results that kick-started this idea, such as Castelnuovo-Mumford regularity, quadric generation of varieties in P^n, and Green's Linear Syzygy Theorem. I'll go over all of the basic definitions and hopefully do lots of examples---in particular, this talk should be accessible to someone taking the intro Algebraic Geometry sequence.<br />
|} <br />
</center><br />
<br />
===March 1===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Asvin G<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
<br />
===March 8===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===March 22===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Kevin Dao<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Enriques-Kodaira Classification and its Influence on MMP<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: There is always more to say than there is time to say it. Let this abstract be an overly optimistic summary. I’ll tell you what the EK classification is, how it is achieved, the relevant development of birational algebraic geometry, and then point towards the difficulties in higher dimensions. I’ll also indicate, where possible and from what I know, the technical tools that are ubiquitous to the topic. If there is time, I will indicate a few problems and directions in either (a) the classification of (non-algebraic) surfaces, (b) rational curves on varieties, (c) major results of the MMP itself.<br />
|} <br />
</center><br />
<br />
===March 29===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Peter Yi Wei<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===April 5===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Colin Crowley (Maybe)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: TBD<br />
<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
<br />
===April 12===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Yunfan He<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Introduction to the Deligne-Illusie theory<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===April 19===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Jacob Wood<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title:<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===April 26===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title:<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===May 3===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Sun Woo Park<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Introduction to Newton Polygon<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2023&diff=24706Graduate Algebraic Geometry Seminar Spring 20232023-03-27T17:40:54Z<p>Jcobb2: </p>
<hr />
<div>'''When:''' 4:15-5:15 PM on Wednesday.<br />
<br />
'''Where:''' Van Vleck B119<br />
[[Image:newcat.jpg|thumb|220px| Toby the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the [https://hilbert.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&redirect=yes Algebraic Geometry Seminar]. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is [https://groups.google.com/u/2/a/g-groups.wisc.edu/g/gags here].<br />
<br />
''' Organizers: ''' [https://johndcobb.github.io John Cobb], [https://people.math.wisc.edu/~yluo237/ Yu (Joey) Luo]<br />
<br />
==Give a talk!==<br />
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the [https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar main page]. Sign up [https://forms.gle/XmdJ4hGbxvpbVVwr5 here].<br />
<br />
===Wishlist===<br />
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.<br />
* Hilbert Schemes<br />
*Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"<br />
*A History of the Weil Conjectures<br />
*A pre talk for any other upcoming talk<br />
*Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).<br />
<br />
==Being an audience member==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
*Do Not Speak For/Over the Speaker<br />
*Ask Questions Appropriately<br />
<br />
==Talks==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center" |'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title'''<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#January 31|January 31]]<br />
| bgcolor="#C6D46E" | Mahrud Sayrafi<br />
| bgcolor="#BCE2FE" | Bounding the Multigraded Regularity of Powers of Ideals<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 1|February 1]]<br />
| bgcolor="#C6D46E" |John Cobb<br />
| bgcolor="#BCE2FE" |Introduction to Intersection Theory<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 8|February 8]]<br />
| bgcolor="#C6D46E" |Yiyu Wang<br />
| bgcolor="#BCE2FE" |An introduction to Macpherson's Chern classes<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 15|February 15]]<br />
| bgcolor="#C6D46E" |Alex Hof <br />
| bgcolor="#BCE2FE" |Normal Cones in Algebraic Geometry<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#February 22|February 22]]<br />
| bgcolor="#C6D46E" |Maya Banks<br />
| bgcolor="#BCE2FE" |Syzygies of Projective Varieties<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 3|March 1]]<br />
| bgcolor="#C6D46E" |Asvin G<br />
| bgcolor="#BCE2FE" |TBD<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 10|March 8]]<br />
| bgcolor="#C6D46E" |<br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 24|March 22]]<br />
| bgcolor="#C6D46E" |Kevin Dao<br />
| bgcolor="#BCE2FE" | Enriques-Kodaira Classification and its Influence on MMP<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#March 31|March 29]]<br />
| bgcolor="#C6D46E" |Peter Yi Wei<br />
| bgcolor="#BCE2FE" |TBD<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#April 7|April 5]]<br />
| bgcolor="#C6D46E" |Dima Arinkin<br />
| bgcolor="#BCE2FE" |Hitchin Fibration<br />
|-<br />
| bgcolor="#E0E0E0" |[[Graduate Algebraic Geometry Seminar Spring 2023#April 14|April 12]]<br />
| bgcolor="#C6D46E" |Yunfan He<br />
| bgcolor="#BCE2FE" |Introduction to the Deligne-Illusie theory<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#April 21|April 19]]<br />
| bgcolor="#C6D46E" | Jacob Wood<br />
| bgcolor="#BCE2FE" |K-Theory or something<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#April 28|April 26]]<br />
| bgcolor="#C6D46E" | <br />
| bgcolor="#BCE2FE" |<br />
|-<br />
| bgcolor="#E0E0E0" | [[Graduate Algebraic Geometry Seminar Spring 2023#May 5|May 3]]<br />
| bgcolor="#C6D46E" | Sun Woo Park<br />
| bgcolor="#BCE2FE" |Introduction to Newton Polygon<br />
|}<br />
</center><br />
<br />
===January 31===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | Mahrud Sayrafi<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Bounding the Multigraded Regularity of Powers of Ideals<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: Building on a result of Swanson, Cutkosky-Herzog-Trung and Kodiyalam described the surprisingly predictable asymptotic behavior of Castelnuovo--Mumford regularity for powers of ideals on a projective space P^n: given an ideal I, there exist integers d and e such that for large enough n the regularity of I^n is exactly dn+e.<br />
Through a medley of examples we will see why asking the same question about an ideal I in the total coordinate ring S of a smooth projective toric variety X is interesting. After that I will summarize the ideas and methods we used to bound the region reg(I^n) as a subset of Pic(X) by proving that it contains a translate of reg(S) and is contained in a translate of Nef(X), with each bound translating by a fixed vector as n increases. Along the way will see some surprising behavior for multigraded regularity of modules. This is joint work with Juliette Bruce and Lauren Cranton Heller.<br />
|} <br />
</center><br />
<br />
===February 1===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | John Cobb<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Introduction to Intersection Theory<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: In this <s>advertisement</s> talk, I'd like to talk about some methods used in enumerative geometry. I'll define what a Chow ring is, count some things with it, and tell you why you should read "3264 and all that" this semester with me. <br />
|} <br />
</center><br />
<br />
===February 8===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | Yiyu Wang<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: An introduction to Macpherson's Chern classes<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: In this talk, I will start from a formula of the Euler characteristic number of a degree d smooth hypersurface in P^n and discuss how to generalize this formula to the singular case. This naturally leads to the notion of the Chern classes of a singular space. I will briefly introduce Macpherson's Chern classes which is a natural generalization of the ordinary Chern class and how to calculate these classes.<br />
|} <br />
</center><br />
<br />
===February 15===<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
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| bgcolor="#A6B658" align="center" style="font-size:125%" |Alex Hof<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Normal Cones in Algebraic Geometry<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: In this talk, we'll go over the definition of the normal cone of a closed subscheme, explore the geometric intuition behind it via a construction called the Rees algebra, and explain how it can be used to give geometric characterizations of apparently algebraic notions such as flatness and depth.<br />
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===February 22===<br />
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{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Maya Banks<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Syzygies of Projective Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: The general slogan for the study of syzygies in geometry is that "geometric information about a projective variety is reflected in its sygygies." In this talk, we'll discuss some of the early results that kick-started this idea, such as Castelnuovo-Mumford regularity, quadric generation of varieties in P^n, and Green's Linear Syzygy Theorem. I'll go over all of the basic definitions and hopefully do lots of examples---in particular, this talk should be accessible to someone taking the intro Algebraic Geometry sequence.<br />
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===March 1===<br />
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|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Asvin G<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
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</center><br />
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===March 8===<br />
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{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: <br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
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</center><br />
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===March 22===<br />
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{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Kevin Dao<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Enriques-Kodaira Classification and its Influence on MMP<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: There is always more to say than there is time to say it. Let this abstract be an overly optimistic summary. I’ll tell you what the EK classification is, how it is achieved, the relevant development of birational algebraic geometry, and then point towards the difficulties in higher dimensions. I’ll also indicate, where possible and from what I know, the technical tools that are ubiquitous to the topic. If there is time, I will indicate a few problems and directions in either (a) the classification of (non-algebraic) surfaces, (b) rational curves on varieties, (c) major results of the MMP itself.<br />
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</center><br />
<br />
===March 29===<br />
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{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Peter Yi Wei<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
===April 5===<br />
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|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Colin Crowley (Maybe)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: TBD<br />
<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract:<br />
|} <br />
</center><br />
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===April 12===<br />
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|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Yunfan He<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Introduction to the Deligne-Illusie theory<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
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</center><br />
<br />
===April 19===<br />
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| bgcolor="#A6B658" align="center" style="font-size:125%" |Jacob Wood<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title:<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
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</center><br />
<br />
===April 26===<br />
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{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title:<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
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</center><br />
<br />
===May 3===<br />
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{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" |Sun Woo Park<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Title: Introduction to Newton Polygon<br />
|-<br />
| bgcolor="#BCD2EE" |Abstract: <br />
|} <br />
</center><br />
<br />
==Past Semesters==<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2022 Fall 2022]<br />
<br />
[https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2022 Spring 2022]<br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2021 Fall 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2020 Fall 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2020 Spring 2020]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Jcobb2