https://wiki.math.wisc.edu/api.php?action=feedcontributions&user=Spark483&feedformat=atomUW-Math Wiki - User contributions [en]2024-03-29T00:01:56ZUser contributionsMediaWiki 1.39.5https://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2019&diff=16643NTSGrad Spring 20192019-01-17T20:30:06Z<p>Spark483: /* Spring 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B113 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS_Spring_2019_Semester| Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Spring 2019 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | January 22<br />
| bgcolor="#F0B0B0" align="center" | Soumya Sankar<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | January 29<br />
| bgcolor="#F0B0B0" align="center" | Ewan Dalby<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 5<br />
| bgcolor="#F0B0B0" align="center" | Sun Woo Park<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 12<br />
| bgcolor="#F0B0B0" align="center" | TBA<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 19<br />
| bgcolor="#F0B0B0" align="center" | TBA<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 26<br />
| bgcolor="#F0B0B0" align="center" | TBA<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | (Arizona Winter School)<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | (Spring Break)<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | TBA<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | TBA<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | TBA<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 16<br />
| bgcolor="#F0B0B0" align="center" | TBA<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | TBA<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | TBA<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | May 7<br />
| bgcolor="#F0B0B0" align="center" | TBA<br />
| bgcolor="#BCE2FE"| TBA<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Spark483https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16544Graduate Algebraic Geometry Seminar2018-12-09T19:18:18Z<p>Spark483: /* December 12 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie 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. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday 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@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). 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 />
<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 />
<br />
==Ed Dewey's Wish List Of Olde==<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 />
===Famous Theorems===<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 />
__NOTOC__<br />
<br />
== Autumn 2018 ==<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 (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| September 12<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Hodge Theory: One hour closer to understanding what it's about]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 19<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Linear Resolutions of Edge Ideals]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 26<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 26| An Elementary Introduction to Geometric Langlands]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 3<br />
| bgcolor="#C6D46E"| Wanlin Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 3| Gonality of Curves and More]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 10<br />
| bgcolor="#C6D46E"| Ewan Dalby<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 10| A Gentle introduction to Grothendieck's Galois theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 17<br />
| bgcolor="#C6D46E"| Johnnie Han<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 17| Schubert Calculus]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 24<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 24| Quadratic Polynomials]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 31<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 31| How to Parameterize Elliptic Curves and Influence People]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 7<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 7| Morita Duality and Local Duality]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 14<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 14| Homological Projective Duality]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 21<br />
| bgcolor="#C6D46E"| A turkey/Smallpox<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 28<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 30| Deformation Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 5<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 5| One Step Closer to <math>B_{cris}</math>]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 12<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 12| A Survey of Newton Polygons]]<br />
|}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge Theory: One hour closer to understanding what it's about<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
|} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Linear Resolutions of Edge Ideals<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
|} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Elementary Introduction to Geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
|} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Gonality of Curves and More<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
|} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Gentle introduction to Grothendiecks Galois theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
|} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Schubert Calculus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
In this talk, we’ll go back to 19th-century Europe, when enumerative geometric questions like “how many lines intersect a quadric” or “how many lines lie on a cubic surface” were answered without even knowing the intersection pairing existed! We’ll go through the methods of Schubert calculus with examples and talk briefly about Steiner’s conics problem, when a famous mathematician was actually proven completely wrong.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Quadratic Polynomials<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of L-functions to show up, that would be ridiculous.<br />
|} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: How to Parameterize Elliptic Curves and Influence People<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
A classical guide to classifying curves for the geometrically minded grad student. I will assume basically zero AG background.<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Morita duality and local duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract:<br />
<br />
I will explain what it means for a ring to admit a dualizing module and how to construct such for nice local rings.<br />
<br />
|} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Homological Projective Duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce the derived category with the goal of undestanding Kuznetsov's HPD, a mysterious phenomenon which has produced a great number of examples and theorems in AG. We will give a demonstration of the duality in the case of an intersection of quadrics. <br />
|} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin G'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Deformation Theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will explain what deformation theory is and how to use it by doing a few examples.<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: One Step Closet to <math>B_{cris}</math><br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will talk about various comparison theorems in <math>p</math>-adic cohomology, and time permitting, describe the crystalline side of things in greater detail.<br />
|} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Sun Woo Park'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Survey of Newton Polygons<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will give a survey on how understanding newton polygons can be useful in solving many different problems in algebraic geometry: from the proof of p-adic Weierstrass Formula to the re-formulization of Tate's Algorithm for elliptic curves. (Since I will focus on providing various applications of newton polygons, I will not be able to present rigorous proofs to most of the statements I will make in this talk.)<br />
<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<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>Spark483https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16543Graduate Algebraic Geometry Seminar2018-12-09T19:18:06Z<p>Spark483: /* December 12 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie 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. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday 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@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). 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 />
<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 />
<br />
==Ed Dewey's Wish List Of Olde==<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 />
===Famous Theorems===<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 />
__NOTOC__<br />
<br />
== Autumn 2018 ==<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 (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| September 12<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Hodge Theory: One hour closer to understanding what it's about]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 19<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Linear Resolutions of Edge Ideals]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 26<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 26| An Elementary Introduction to Geometric Langlands]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 3<br />
| bgcolor="#C6D46E"| Wanlin Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 3| Gonality of Curves and More]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 10<br />
| bgcolor="#C6D46E"| Ewan Dalby<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 10| A Gentle introduction to Grothendieck's Galois theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 17<br />
| bgcolor="#C6D46E"| Johnnie Han<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 17| Schubert Calculus]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 24<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 24| Quadratic Polynomials]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 31<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 31| How to Parameterize Elliptic Curves and Influence People]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 7<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 7| Morita Duality and Local Duality]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 14<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 14| Homological Projective Duality]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 21<br />
| bgcolor="#C6D46E"| A turkey/Smallpox<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 28<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 30| Deformation Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 5<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 5| One Step Closer to <math>B_{cris}</math>]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 12<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 12| A Survey of Newton Polygons]]<br />
|}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge Theory: One hour closer to understanding what it's about<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
|} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Linear Resolutions of Edge Ideals<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
|} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Elementary Introduction to Geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
|} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Gonality of Curves and More<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
|} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Gentle introduction to Grothendiecks Galois theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
|} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Schubert Calculus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
In this talk, we’ll go back to 19th-century Europe, when enumerative geometric questions like “how many lines intersect a quadric” or “how many lines lie on a cubic surface” were answered without even knowing the intersection pairing existed! We’ll go through the methods of Schubert calculus with examples and talk briefly about Steiner’s conics problem, when a famous mathematician was actually proven completely wrong.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Quadratic Polynomials<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of L-functions to show up, that would be ridiculous.<br />
|} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: How to Parameterize Elliptic Curves and Influence People<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
A classical guide to classifying curves for the geometrically minded grad student. I will assume basically zero AG background.<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Morita duality and local duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract:<br />
<br />
I will explain what it means for a ring to admit a dualizing module and how to construct such for nice local rings.<br />
<br />
|} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Homological Projective Duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce the derived category with the goal of undestanding Kuznetsov's HPD, a mysterious phenomenon which has produced a great number of examples and theorems in AG. We will give a demonstration of the duality in the case of an intersection of quadrics. <br />
|} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin G'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Deformation Theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will explain what deformation theory is and how to use it by doing a few examples.<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: One Step Closet to <math>B_{cris}</math><br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will talk about various comparison theorems in <math>p</math>-adic cohomology, and time permitting, describe the crystalline side of things in greater detail.<br />
|} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Sun Woo Park'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Survey of Newton Polygons<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will give a survey on how understanding newton polygons can be useful in solving many different problems in algebraic geometry: from the proof of p-adic Weierstrass Formula to the re-formulization of Tate's Algorithm for elliptic curves. (Since I will focus on providing various applications of newton polygons, I will not be able to present rigorous proofs to most of the statements I will make in this talk.)<br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<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>Spark483https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16481Graduate Algebraic Geometry Seminar2018-11-28T22:09:47Z<p>Spark483: /* December 12 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie 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. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday 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@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). 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 />
<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 />
<br />
==Ed Dewey's Wish List Of Olde==<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 />
===Famous Theorems===<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 />
__NOTOC__<br />
<br />
== Autumn 2018 ==<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 (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| September 12<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Hodge Theory: One hour closer to understanding what it's about]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 19<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Linear Resolutions of Edge Ideals]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 26<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 26| An Elementary Introduction to Geometric Langlands]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 3<br />
| bgcolor="#C6D46E"| Wanlin Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 3| Gonality of Curves and More]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 10<br />
| bgcolor="#C6D46E"| Ewan Dalby<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 10| A Gentle introduction to Grothendieck's Galois theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 17<br />
| bgcolor="#C6D46E"| Johnnie Han<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 17| Schubert Calculus]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 24<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 24| Quadratic Polynomials]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 31<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 31| How to Parameterize Elliptic Curves and Influence People]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 7<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 7| Morita Duality and Local Duality]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 14<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 14| Homological Projective Duality]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 21<br />
| bgcolor="#C6D46E"| A turkey/Smallpox<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 28<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 30| Deformation Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 5<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 5| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 12<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 12| A Survey of Newton Polygons]]<br />
|}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge Theory: One hour closer to understanding what it's about<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
|} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Linear Resolutions of Edge Ideals<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
|} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Elementary Introduction to Geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
|} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Gonality of Curves and More<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
|} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Gentle introduction to Grothendiecks Galois theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
|} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Schubert Calculus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
In this talk, we’ll go back to 19th-century Europe, when enumerative geometric questions like “how many lines intersect a quadric” or “how many lines lie on a cubic surface” were answered without even knowing the intersection pairing existed! We’ll go through the methods of Schubert calculus with examples and talk briefly about Steiner’s conics problem, when a famous mathematician was actually proven completely wrong.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Quadratic Polynomials<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of L-functions to show up, that would be ridiculous.<br />
|} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: How to Parameterize Elliptic Curves and Influence People<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
A classical guide to classifying curves for the geometrically minded grad student. I will assume basically zero AG background.<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Morita duality and local duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract:<br />
<br />
I will explain what it means for a ring to admit a dualizing module and how to construct such for nice local rings.<br />
<br />
|} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Homological Projective Duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce the derived category with the goal of undestanding Kuznetsov's HPD, a mysterious phenomenon which has produced a great number of examples and theorems in AG. We will give a demonstration of the duality in the case of an intersection of quadrics. <br />
|} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin G'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Deformation Theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will explain what deformation theory is and how to use it by doing a few examples.<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Sun Woo Park'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Survey of Newton Polygons<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<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>Spark483https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16480Graduate Algebraic Geometry Seminar2018-11-28T22:09:33Z<p>Spark483: /* December 12 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie 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. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday 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@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). 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 />
<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 />
<br />
==Ed Dewey's Wish List Of Olde==<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 />
===Famous Theorems===<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 />
__NOTOC__<br />
<br />
== Autumn 2018 ==<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 (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| September 12<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Hodge Theory: One hour closer to understanding what it's about]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 19<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Linear Resolutions of Edge Ideals]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 26<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 26| An Elementary Introduction to Geometric Langlands]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 3<br />
| bgcolor="#C6D46E"| Wanlin Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 3| Gonality of Curves and More]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 10<br />
| bgcolor="#C6D46E"| Ewan Dalby<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 10| A Gentle introduction to Grothendieck's Galois theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 17<br />
| bgcolor="#C6D46E"| Johnnie Han<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 17| Schubert Calculus]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 24<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 24| Quadratic Polynomials]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 31<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 31| How to Parameterize Elliptic Curves and Influence People]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 7<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 7| Morita Duality and Local Duality]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 14<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 14| Homological Projective Duality]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 21<br />
| bgcolor="#C6D46E"| A turkey/Smallpox<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 28<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 30| Deformation Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 5<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 5| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 12<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 12| A Survey of Newton Polygons]]<br />
|}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge Theory: One hour closer to understanding what it's about<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
|} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Linear Resolutions of Edge Ideals<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
|} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Elementary Introduction to Geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
|} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Gonality of Curves and More<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
|} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Gentle introduction to Grothendiecks Galois theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
|} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Schubert Calculus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
In this talk, we’ll go back to 19th-century Europe, when enumerative geometric questions like “how many lines intersect a quadric” or “how many lines lie on a cubic surface” were answered without even knowing the intersection pairing existed! We’ll go through the methods of Schubert calculus with examples and talk briefly about Steiner’s conics problem, when a famous mathematician was actually proven completely wrong.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Quadratic Polynomials<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of L-functions to show up, that would be ridiculous.<br />
|} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: How to Parameterize Elliptic Curves and Influence People<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
A classical guide to classifying curves for the geometrically minded grad student. I will assume basically zero AG background.<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Morita duality and local duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract:<br />
<br />
I will explain what it means for a ring to admit a dualizing module and how to construct such for nice local rings.<br />
<br />
|} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Homological Projective Duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce the derived category with the goal of undestanding Kuznetsov's HPD, a mysterious phenomenon which has produced a great number of examples and theorems in AG. We will give a demonstration of the duality in the case of an intersection of quadrics. <br />
|} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin G'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Deformation Theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will explain what deformation theory is and how to use it by doing a few examples.<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | ''Sun Woo Park''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Survey of Newton Polygons<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<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>Spark483https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16479Graduate Algebraic Geometry Seminar2018-11-28T22:09:10Z<p>Spark483: /* December 12 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie 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. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday 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@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). 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 />
<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 />
<br />
==Ed Dewey's Wish List Of Olde==<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 />
===Famous Theorems===<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 />
__NOTOC__<br />
<br />
== Autumn 2018 ==<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 (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| September 12<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Hodge Theory: One hour closer to understanding what it's about]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 19<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Linear Resolutions of Edge Ideals]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 26<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 26| An Elementary Introduction to Geometric Langlands]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 3<br />
| bgcolor="#C6D46E"| Wanlin Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 3| Gonality of Curves and More]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 10<br />
| bgcolor="#C6D46E"| Ewan Dalby<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 10| A Gentle introduction to Grothendieck's Galois theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 17<br />
| bgcolor="#C6D46E"| Johnnie Han<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 17| Schubert Calculus]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 24<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 24| Quadratic Polynomials]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 31<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 31| How to Parameterize Elliptic Curves and Influence People]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 7<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 7| Morita Duality and Local Duality]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 14<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 14| Homological Projective Duality]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 21<br />
| bgcolor="#C6D46E"| A turkey/Smallpox<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 28<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 30| Deformation Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 5<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 5| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 12<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 12| A Survey of Newton Polygons]]<br />
|}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge Theory: One hour closer to understanding what it's about<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
|} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Linear Resolutions of Edge Ideals<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
|} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Elementary Introduction to Geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
|} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Gonality of Curves and More<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
|} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Gentle introduction to Grothendiecks Galois theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
|} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Schubert Calculus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
In this talk, we’ll go back to 19th-century Europe, when enumerative geometric questions like “how many lines intersect a quadric” or “how many lines lie on a cubic surface” were answered without even knowing the intersection pairing existed! We’ll go through the methods of Schubert calculus with examples and talk briefly about Steiner’s conics problem, when a famous mathematician was actually proven completely wrong.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Quadratic Polynomials<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of L-functions to show up, that would be ridiculous.<br />
|} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: How to Parameterize Elliptic Curves and Influence People<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
A classical guide to classifying curves for the geometrically minded grad student. I will assume basically zero AG background.<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Morita duality and local duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract:<br />
<br />
I will explain what it means for a ring to admit a dualizing module and how to construct such for nice local rings.<br />
<br />
|} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Homological Projective Duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce the derived category with the goal of undestanding Kuznetsov's HPD, a mysterious phenomenon which has produced a great number of examples and theorems in AG. We will give a demonstration of the duality in the case of an intersection of quadrics. <br />
|} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin G'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Deformation Theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will explain what deformation theory is and how to use it by doing a few examples.<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Survey of Newton Polygons<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<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>Spark483https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16478Graduate Algebraic Geometry Seminar2018-11-28T22:08:59Z<p>Spark483: /* Autumn 2018 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie 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. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday 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@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). 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 />
<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 />
<br />
==Ed Dewey's Wish List Of Olde==<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 />
===Famous Theorems===<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 />
__NOTOC__<br />
<br />
== Autumn 2018 ==<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 (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| September 12<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Hodge Theory: One hour closer to understanding what it's about]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 19<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Linear Resolutions of Edge Ideals]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 26<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 26| An Elementary Introduction to Geometric Langlands]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 3<br />
| bgcolor="#C6D46E"| Wanlin Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 3| Gonality of Curves and More]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 10<br />
| bgcolor="#C6D46E"| Ewan Dalby<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 10| A Gentle introduction to Grothendieck's Galois theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 17<br />
| bgcolor="#C6D46E"| Johnnie Han<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 17| Schubert Calculus]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 24<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 24| Quadratic Polynomials]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 31<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 31| How to Parameterize Elliptic Curves and Influence People]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 7<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 7| Morita Duality and Local Duality]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 14<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 14| Homological Projective Duality]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 21<br />
| bgcolor="#C6D46E"| A turkey/Smallpox<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 28<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 30| Deformation Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 5<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 5| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 12<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 12| A Survey of Newton Polygons]]<br />
|}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge Theory: One hour closer to understanding what it's about<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
|} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Linear Resolutions of Edge Ideals<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
|} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Elementary Introduction to Geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
|} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Gonality of Curves and More<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
|} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Gentle introduction to Grothendiecks Galois theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
|} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Schubert Calculus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
In this talk, we’ll go back to 19th-century Europe, when enumerative geometric questions like “how many lines intersect a quadric” or “how many lines lie on a cubic surface” were answered without even knowing the intersection pairing existed! We’ll go through the methods of Schubert calculus with examples and talk briefly about Steiner’s conics problem, when a famous mathematician was actually proven completely wrong.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Quadratic Polynomials<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of L-functions to show up, that would be ridiculous.<br />
|} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: How to Parameterize Elliptic Curves and Influence People<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
A classical guide to classifying curves for the geometrically minded grad student. I will assume basically zero AG background.<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Morita duality and local duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract:<br />
<br />
I will explain what it means for a ring to admit a dualizing module and how to construct such for nice local rings.<br />
<br />
|} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Homological Projective Duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce the derived category with the goal of undestanding Kuznetsov's HPD, a mysterious phenomenon which has produced a great number of examples and theorems in AG. We will give a demonstration of the duality in the case of an intersection of quadrics. <br />
|} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin G'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Deformation Theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will explain what deformation theory is and how to use it by doing a few examples.<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Survey on Newton Polygons<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<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>Spark483https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16477Graduate Algebraic Geometry Seminar2018-11-28T22:08:15Z<p>Spark483: /* Spring 2017 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie 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. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday 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@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). 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 />
<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 />
<br />
==Ed Dewey's Wish List Of Olde==<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 />
===Famous Theorems===<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 />
__NOTOC__<br />
<br />
== Autumn 2018 ==<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 (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| September 12<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Hodge Theory: One hour closer to understanding what it's about]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 19<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Linear Resolutions of Edge Ideals]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 26<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 26| An Elementary Introduction to Geometric Langlands]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 3<br />
| bgcolor="#C6D46E"| Wanlin Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 3| Gonality of Curves and More]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 10<br />
| bgcolor="#C6D46E"| Ewan Dalby<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 10| A Gentle introduction to Grothendieck's Galois theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 17<br />
| bgcolor="#C6D46E"| Johnnie Han<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 17| Schubert Calculus]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 24<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 24| Quadratic Polynomials]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 31<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 31| How to Parameterize Elliptic Curves and Influence People]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 7<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 7| Morita Duality and Local Duality]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 14<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 14| Homological Projective Duality]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 21<br />
| bgcolor="#C6D46E"| A turkey/Smallpox<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 28<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 30| Deformation Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 5<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 5| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 12<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 12| A Survey on Newton Polygons]]<br />
|}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge Theory: One hour closer to understanding what it's about<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
|} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Linear Resolutions of Edge Ideals<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
|} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Elementary Introduction to Geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
|} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Gonality of Curves and More<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
|} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Gentle introduction to Grothendiecks Galois theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
|} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Schubert Calculus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
In this talk, we’ll go back to 19th-century Europe, when enumerative geometric questions like “how many lines intersect a quadric” or “how many lines lie on a cubic surface” were answered without even knowing the intersection pairing existed! We’ll go through the methods of Schubert calculus with examples and talk briefly about Steiner’s conics problem, when a famous mathematician was actually proven completely wrong.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Quadratic Polynomials<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of L-functions to show up, that would be ridiculous.<br />
|} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: How to Parameterize Elliptic Curves and Influence People<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
A classical guide to classifying curves for the geometrically minded grad student. I will assume basically zero AG background.<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Morita duality and local duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract:<br />
<br />
I will explain what it means for a ring to admit a dualizing module and how to construct such for nice local rings.<br />
<br />
|} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Homological Projective Duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce the derived category with the goal of undestanding Kuznetsov's HPD, a mysterious phenomenon which has produced a great number of examples and theorems in AG. We will give a demonstration of the duality in the case of an intersection of quadrics. <br />
|} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin G'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Deformation Theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will explain what deformation theory is and how to use it by doing a few examples.<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Survey on Newton Polygons<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<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>Spark483https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16476Graduate Algebraic Geometry Seminar2018-11-28T22:07:40Z<p>Spark483: /* December 12 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie 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. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday 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@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). 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 />
<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 />
<br />
==Ed Dewey's Wish List Of Olde==<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 />
===Famous Theorems===<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 />
__NOTOC__<br />
<br />
== Spring 2017 ==<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 (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| September 12<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Hodge Theory: One hour closer to understanding what it's about]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 19<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Linear Resolutions of Edge Ideals]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 26<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 26| An Elementary Introduction to Geometric Langlands]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 3<br />
| bgcolor="#C6D46E"| Wanlin Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 3| Gonality of Curves and More]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 10<br />
| bgcolor="#C6D46E"| Ewan Dalby<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 10| A Gentle introduction to Grothendieck's Galois theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 17<br />
| bgcolor="#C6D46E"| Johnnie Han<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 17| Schubert Calculus]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 24<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 24| Quadratic Polynomials]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 31<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 31| How to Parameterize Elliptic Curves and Influence People]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 7<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 7| Morita Duality and Local Duality]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 14<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 14| Homological Projective Duality]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 21<br />
| bgcolor="#C6D46E"| A turkey/Smallpox<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 28<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 30| Deformation Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 5<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 5| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 12<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 12| TBD]]<br />
|}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge Theory: One hour closer to understanding what it's about<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
|} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Linear Resolutions of Edge Ideals<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
|} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Elementary Introduction to Geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
|} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Gonality of Curves and More<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
|} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Gentle introduction to Grothendiecks Galois theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
|} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Schubert Calculus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
In this talk, we’ll go back to 19th-century Europe, when enumerative geometric questions like “how many lines intersect a quadric” or “how many lines lie on a cubic surface” were answered without even knowing the intersection pairing existed! We’ll go through the methods of Schubert calculus with examples and talk briefly about Steiner’s conics problem, when a famous mathematician was actually proven completely wrong.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Quadratic Polynomials<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of L-functions to show up, that would be ridiculous.<br />
|} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: How to Parameterize Elliptic Curves and Influence People<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
A classical guide to classifying curves for the geometrically minded grad student. I will assume basically zero AG background.<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Morita duality and local duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract:<br />
<br />
I will explain what it means for a ring to admit a dualizing module and how to construct such for nice local rings.<br />
<br />
|} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Homological Projective Duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce the derived category with the goal of undestanding Kuznetsov's HPD, a mysterious phenomenon which has produced a great number of examples and theorems in AG. We will give a demonstration of the duality in the case of an intersection of quadrics. <br />
|} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin G'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Deformation Theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will explain what deformation theory is and how to use it by doing a few examples.<br />
|} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Survey on Newton Polygons<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<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>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16271AMS Student Chapter Seminar2018-10-24T22:30:06Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: What does a group look like?<br />
<br />
Abstract: In geometric group theory, we often try to understand groups by understanding the metric spaces on which the groups act geometrically. For example, Z^2 acts on R^2 in a nice way, so we can think of the group Z^2 instead as the metric space R^2.<br />
<br />
We will try to find (and draw) such a metric space for the solvable Baumslag-Solitar groups BS(1,n). Then we will briefly discuss what this geometric picture tells us about the groups.<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induction-Restriction Operators<br />
<br />
Abstract: Given a "nice enough" finite descending sequence of groups <math> G_n \supsetneq G_{n-1} \supsetneq \cdots \supsetneq G_1 \supsetneq \{e\} </math>, we can play around with the relations between induced and restricted representations. We will construct a formal <math> \mathbb{Z} </math>-module of induction-restriction operators on a finite descending sequence of groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that the formal ring <math> IR_{\{G_i\}} </math> is a commutative polynomial ring over <math> \mathbb{Z} </math>. We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 </math>. (Apart from the talk, I'll also prepare some treats in celebration of Halloween.)<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16270AMS Student Chapter Seminar2018-10-24T22:29:20Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: What does a group look like?<br />
<br />
Abstract: In geometric group theory, we often try to understand groups by understanding the metric spaces on which the groups act geometrically. For example, Z^2 acts on R^2 in a nice way, so we can think of the group Z^2 instead as the metric space R^2.<br />
<br />
We will try to find (and draw) such a metric space for the solvable Baumslag-Solitar groups BS(1,n). Then we will briefly discuss what this geometric picture tells us about the groups.<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induction-Restriction Operators<br />
<br />
Abstract: Given a "nice enough" finite descending sequence of groups <math> G_n \supsetneq G_{n-1} \supsetneq \cdots \supsetneq G_1 \supsetneq \{e\} </math>, we can play around with the relations between induced and restricted representations. We will construct a formal <math> \mathbb{Z} </math>-module of induction-restriction operators on a finite descending sequence of groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that the formal ring <math> IR_{\{G_i\}} </math> is a commutative polynomial ring over <math> \mathbb{Z} </math>. We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 </math>. (Apart from the talk, I'll also prepare some treats in celebration of Halloween other than donuts.)<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16269AMS Student Chapter Seminar2018-10-24T22:29:03Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: What does a group look like?<br />
<br />
Abstract: In geometric group theory, we often try to understand groups by understanding the metric spaces on which the groups act geometrically. For example, Z^2 acts on R^2 in a nice way, so we can think of the group Z^2 instead as the metric space R^2.<br />
<br />
We will try to find (and draw) such a metric space for the solvable Baumslag-Solitar groups BS(1,n). Then we will briefly discuss what this geometric picture tells us about the groups.<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induction-Restriction Operators<br />
<br />
Abstract: Given a "nice enough" finite descending sequence of groups <math> G_n \supset G_{n-1} \supset \cdots \supset G_1 \supset \{e\} </math>, we can play around with the relations between induced and restricted representations. We will construct a formal <math> \mathbb{Z} </math>-module of induction-restriction operators on a finite descending sequence of groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that the formal ring <math> IR_{\{G_i\}} </math> is a commutative polynomial ring over <math> \mathbb{Z} </math>. We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 </math>. (Apart from the talk, I'll also prepare some treats in celebration of Halloween other than donuts.)<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16268AMS Student Chapter Seminar2018-10-24T22:28:13Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: What does a group look like?<br />
<br />
Abstract: In geometric group theory, we often try to understand groups by understanding the metric spaces on which the groups act geometrically. For example, Z^2 acts on R^2 in a nice way, so we can think of the group Z^2 instead as the metric space R^2.<br />
<br />
We will try to find (and draw) such a metric space for the solvable Baumslag-Solitar groups BS(1,n). Then we will briefly discuss what this geometric picture tells us about the groups.<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induction-Restriction Operators<br />
<br />
Abstract: Given a "nice enough" finite descending sequence of groups, we can play around with the relations between induced and restricted representations. We will construct a formal <math> \mathbb{Z} </math>-module of induction-restriction operators on a finite descending sequence of groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that the formal ring <math> IR_{\{G_i\}} </math> is a commutative polynomial ring over <math> \mathbb{Z} </math>. We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 </math>. (Apart from the talk, I'll also prepare some treats in celebration of Halloween other than donuts.)<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16267AMS Student Chapter Seminar2018-10-24T22:25:04Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: What does a group look like?<br />
<br />
Abstract: In geometric group theory, we often try to understand groups by understanding the metric spaces on which the groups act geometrically. For example, Z^2 acts on R^2 in a nice way, so we can think of the group Z^2 instead as the metric space R^2.<br />
<br />
We will try to find (and draw) such a metric space for the solvable Baumslag-Solitar groups BS(1,n). Then we will briefly discuss what this geometric picture tells us about the groups.<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induction-Restriction Operators on a Finite Descending Sequence of Groups<br />
<br />
Abstract: Given a "nice enough" finite descending sequence of groups, we can play around with the relations between induced and restricted representations. We will construct a formal <math> \mathbb{Z} </math>-module of induction-restriction operators on a finite descending sequence of groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that the formal ring <math> IR_{\{G_i\}} </math> is a commutative polynomial ring over <math> \mathbb{Z} </math>. We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 </math>.<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16266AMS Student Chapter Seminar2018-10-24T22:24:49Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: What does a group look like?<br />
<br />
Abstract: In geometric group theory, we often try to understand groups by understanding the metric spaces on which the groups act geometrically. For example, Z^2 acts on R^2 in a nice way, so we can think of the group Z^2 instead as the metric space R^2.<br />
<br />
We will try to find (and draw) such a metric space for the solvable Baumslag-Solitar groups BS(1,n). Then we will briefly discuss what this geometric picture tells us about the groups.<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induction-Restriction Operators on a Finite Descending Sequence of Groups<br />
<br />
Abstract: Given a "nice enough" finite descending sequence of groups, we can play around quite a lot with the relations between induced and restricted representations. We will construct a formal <math> \mathbb{Z} </math>-module of induction-restriction operators on a finite descending sequence of groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that the formal ring <math> IR_{\{G_i\}} </math> is a commutative polynomial ring over <math> \mathbb{Z} </math>. We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 </math>.<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16265AMS Student Chapter Seminar2018-10-24T22:07:48Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: What does a group look like?<br />
<br />
Abstract: In geometric group theory, we often try to understand groups by understanding the metric spaces on which the groups act geometrically. For example, Z^2 acts on R^2 in a nice way, so we can think of the group Z^2 instead as the metric space R^2.<br />
<br />
We will try to find (and draw) such a metric space for the solvable Baumslag-Solitar groups BS(1,n). Then we will briefly discuss what this geometric picture tells us about the groups.<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induction-Restriction Operators on a Finite Descending Sequence of Groups<br />
<br />
Abstract: We will state what induced and restricted representations are. We will then construct a formal <math> \mathbb{Z} </math>-module of induction-restriction operators on a finite descending sequence of groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that the formal ring <math> IR_{\{G_i\}} </math> is a commutative polynomial ring over <math> \mathbb{Z} </math>. We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 </math>.<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16250AMS Student Chapter Seminar2018-10-21T23:49:30Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induction-Restriction Operators on a Finite Descending Sequence of Groups<br />
<br />
Abstract: We will state what induced and restricted representations are. We will then construct a formal <math> \mathbb{Z} </math>-module of induction-restriction operators on a finite descending sequence of groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that under certain nice conditions, the formal ring <math> IR_{\{G_i\}} </math> is isomorphic to a polynomial ring <math> \mathbb{Z}[x]/J </math> for some ideal <math> J \subset \mathbb{Z}[x] </math>. We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 </math>.<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16249AMS Student Chapter Seminar2018-10-21T23:29:10Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induction-Restriction Operators on a Finite Descending Sequence of Groups<br />
<br />
Abstract: We will state what induced and restricted representations are. We will then construct a formal <math> \mathbb{Z} </math>-module of induction-restriction operators on a finite descending sequence of groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that under certain nice conditions, the formal ring <math> IR_{\{G_i\}} </math> is isomorphic to a polynomial ring <math> \mathbb{Z}[x]/J </math> for some ideal <math> J \subset \mathbb{Z}[x] </math>. We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 = \{1\} </math>.<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16248AMS Student Chapter Seminar2018-10-21T23:28:17Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induction-Restriction Operators on a Finite Descending Sequence of Finite Groups<br />
<br />
Abstract: We will state what induced and restricted representations are. We will then construct a formal <math> \mathbb{Z} </math>-module of induction-restriction operators on a finite descending sequence of finite groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that the formal ring <math> IR_{\{G_i\}} </math> is isomorphic to a polynomial ring <math> \mathbb{Z}[x]/J </math> for some ideal <math> J \subset \mathbb{Z}[x] </math>. We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 = \{1\} </math>.<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16247AMS Student Chapter Seminar2018-10-21T23:27:32Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induction-Restriction Operators on a Finite Descending Sequence of Finite Groups<br />
<br />
Abstract: We will introduce what induced and restricted representations are. We will then construct a formal <math> \mathbb{Z} </math>-module of induction-restriction operators on a finite descending sequence of finite groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that the formal ring <math> IR_{\{G_i\}} </math> is isomorphic to a polynomial ring <math> \mathbb{Z}[x]/J </math> for some ideal <math> J \subset \mathbb{Z}[x] </math>. We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 = \{1\} </math>.<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16246AMS Student Chapter Seminar2018-10-21T23:25:16Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induction-Restriction Operators on a Finite Descending Sequence of Finite Groups<br />
<br />
Abstract: We will introduce what induced and restricted representations of a finite group <math> G </math> is. We will then construct a formal <math> \mathbb{Z} </math>-module of induction-restriction operators on a finite descending sequence of finite groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that the formal ring <math> IR_{\{G_i\}} </math> is isomorphic to a polynomial ring <math> \mathbb{Z}[x]/J </math> for some ideal <math> J \subset \mathbb{Z}[x] </math>. We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 = \{1\} </math>.<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16245AMS Student Chapter Seminar2018-10-21T23:25:00Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induction-Restriction Operators on a Finite Descending Sequence of Finite Groups<br />
<br />
Abstract: We will introduce what induced and restricted representations of a finite group <math> G </math> is. We will then construct a formal <math> \mathbb{Z} </math>-module of induction-restriction operators on a finite descending sequence of finite groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that the formal ring <math> IR_{\{G_i\}} </math> is isomorphic to a polynomial ring <math> \mathbb{Z}[x]/I </math> for some ideal <math> I \subset \mathbb{Z}[x] </math>. We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 = \{1\} </math>.<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16244AMS Student Chapter Seminar2018-10-21T23:23:07Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induction-Restriction Operators on a Finite Descending Sequence of Finite Groups<br />
<br />
Abstract: We will introduce what induced and restricted representations of a finite group <math> G </math> is. We will then construct a formal ring of induction-restriction operators on a finite descending sequence of finite groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that the formal ring <math> IR_{\{G_i\}} </math> is in fact a commutative polynomial ring over <math> \mathbb{Z} </math> of 1 variable. We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 = \{1\} </math>.<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16243AMS Student Chapter Seminar2018-10-21T23:22:35Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induced and Restricted Representations on a Finite Descending Sequence of Finite Groups<br />
<br />
Abstract: We will introduce what induced and restricted representations of a finite group <math> G </math> is. We will then construct a formal ring of induction-restriction operators on a finite descending sequence of finite groups <math> \{G_i\} </math>, written as <math> IR_{\{G_i\}} </math>. The goal of the talk is to show that the formal ring <math> IR_{\{G_i\}} </math> is in fact a commutative polynomial ring over <math> \mathbb{Z} </math> of 1 variable. We will also compute the formal ring <math>IR_{\{S_n\}} </math> for a finite descending sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_1 = \{1\} </math>.<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16242AMS Student Chapter Seminar2018-10-21T23:13:12Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induced and Restricted Representations of a Sequence of Finite Groups<br />
<br />
Abstract: Let <math> G </math> be a finite group. Given a sequence of groups <math> G = G_n \supset G_{n-1} \supset \cdots \supset G_2 \supset G_1 = \{1\} </math>, we can construct a formal ring <math> IR_G </math> of induction-restriction operators on <math> G </math>. (I will state the definition in the talk!) Using Frobenius reciprocity, we will show that the formal ring <math> IR_G </math> is in fact a commutative polynomial ring of 1 variable. If time allows, we will also show that for a sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_2 \supset S_1 = \{1\} </math>, the formal ring <math> IR_{S_n} </math> is isomorphic to a polynomial ring <math> \mathbb{Z}[x]/(f(x)) </math>, where <math>f(x)</math> is a polynomial of degree <math> n </math>.<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16241AMS Student Chapter Seminar2018-10-21T23:12:31Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induced and Restricted Representations of a Sequence of Groups<br />
<br />
Abstract: Let <math> G </math> be a finite group. Given a sequence of groups <math> G = G_n \supset G_{n-1} \supset \cdots \supset G_2 \supset G_1 = \{1\} </math>, we can construct a formal ring <math> IR_G </math> of induction-restriction operators on <math> G </math>. (I will state the definition in the talk!) Using Frobenius reciprocity, we will show that the formal ring <math> IR_G </math> is in fact a commutative polynomial ring of 1 variable. If time allows, we will also show that for a sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_2 \supset S_1 = \{1\} </math>, the formal ring <math> IR_{S_n} </math> is isomorphic to a polynomial ring <math> \mathbb{Z}[x]/(f(x)) </math>, where <math>f(x)</math> is a polynomial of degree <math> n </math>.<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16240AMS Student Chapter Seminar2018-10-21T22:32:32Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induced and Restricted Representations of a Sequence of Groups<br />
<br />
Abstract: Let <math> G </math> be a finite group. Given a sequence of groups <math> G = G_n \supset G_{n-1} \supset \cdots \supset G_2 \supset G_1 = \{1\} </math>, we can construct a formal ring of induction-restriction operators on <math> G </math>, which we denote by <math> IR_G := \mathbb{Z} \langle Ind(Res), Ind^2(Res^2), \cdots, Ind^n(Res^n) \rangle </math>. Using Frobenius reciprocity, we will show that the formal ring <math> IR_G </math> is in fact a commutative polynomial ring of 1 variable. If time allows, we will also show that for a sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_2 \supset S_1 = \{1\} </math>, the formal ring <math> IR_{S_n} </math> is isomorphic to a polynomial ring <math> \mathbb{Z}[x]/(f(x)) </math>, where <math>f(x)</math> is a polynomial of degree <math> n </math>.<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16239AMS Student Chapter Seminar2018-10-21T22:31:15Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induced and Restricted Representations of a Sequence of Groups<br />
<br />
Abstract: Let <math> G </math> be a finite group. Given a sequence of groups <math> G = G_n \supset G_{n-1} \supset \cdots \supset G_2 \supset G_1 = \{1\} </math>, we can construct a formal ring of induction-restriction operators on <math> G </math>, which we denote by <math> \mathbb{Z} \langle Ind(Res), Ind^2(Res^2), \cdots, Ind^n(Res^n) \rangle </math>. Using Frobenius reciprocity, we will show that the formal ring for any finite group <math> G </math> is in fact a commutative polynomial ring of 1 variable. If time allows, we will also show that for a sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_2 \supset S_1 = \{1\} </math>, the formal ring of <math> S_n </math> isomorphic to a polynomial ring <math> \mathbb{Z}[x]/(f(x)) </math>, where <math>f(x)</math> is a polynomial of degree <math> n </math>.<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16238AMS Student Chapter Seminar2018-10-21T22:28:59Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induced and Restricted Representations of a Sequence of Groups<br />
<br />
Abstract: Given a sequence of groups <math> G_n \supset G_{n-1} \supset \cdots \supset G_2 \supset G_1 = \{1\} </math>, we can construct a formal ring of induction-restriction operators on <math> G_n </math>, which we denote by <math> \mathbb{Z} \langle Ind(Res), Ind^2(Res^2), \cdots, Ind^n(Res^n) \rangle </math>. Using Frobenius reciprocity, we will show that the formal ring for any group <math> G_n </math> is in fact a commutative polynomial ring of 1 variable. If time allows, we will also show that for a sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_2 \supset S_1 = \{1\} </math>, the formal ring of <math> S_n </math> isomorphic to a polynomial ring <math> \mathbb{Z}[x]/(f(x)) </math>, where <math>f(x)</math> is a polynomial of degree <math> n </math>.<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16237AMS Student Chapter Seminar2018-10-21T22:28:43Z<p>Spark483: /* October 31, Sun Woo Park */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
=== September 26, Vladimir Sotirov ===<br />
<br />
Title: Geometric Algebra<br />
<br />
Abstract: Geometric algebra, developed at the end of the 19th century by Grassman, Clifford, and Lipschitz, is the forgotten progenitor of the linear algebra we use to this day developed by Gibbs and Heaviside.<br />
In this short introduction, I will use geometric algebra to do two things. First, I will construct the field of complex numbers and the division algebra of the quaternions in a coordinate-free way. Second, I will derive the geometric interpretation of complex numbers and quaternions as representations of rotations in 2- and 3-dimensional space. <br />
<br />
=== October 3, Juliette Bruce ===<br />
<br />
Title: Kissing Conics<br />
<br />
Abstract: Have you every wondered how you can easily tell when two plane conics kiss (i.e. are tangent to each other at a point)? If so this talk is for you, if not, well there will be donuts.<br />
<br />
=== October 10, Kurt Ehlert ===<br />
<br />
Title: How to bet when gambling<br />
<br />
Abstract: When gambling, typically casinos have the edge. But sometimes we can gain an edge by counting cards or other means. And sometimes we have an edge in the biggest casino of all: the financial markets. When we do have an advantage, then we still need to decide how much to bet. Bet too little, and we leave money on the table. Bet too much, and we risk financial ruin. We will discuss the "Kelly criterion", which is a betting strategy that is optimal in many senses.<br />
<br />
=== October 17, Bryan Oakley ===<br />
<br />
Title: Mixing rates<br />
<br />
Abstract: Mixing is a necessary step in many areas from biology and atmospheric sciences to smoothies. Because we are impatient, the goal is usually to improve the rate at which a substance homogenizes. In this talk we define and quantify mixing and rates of mixing. We present some history of the field as well as current research and open questions.<br />
<br />
=== October 24, Micky Soule Steinberg ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== October 31, Sun Woo Park ===<br />
<br />
Title: Induced and Restricted Representations of a Sequence of Groups<br />
<br />
Abstract: Given a sequence of groups <math> G_n \supset G_{n-1} \supset \cdots \supset G_2 \supset G_1 = \{1\} </math>, we can construct a formal ring of induction-restriction operators on <math> S_n </math>, which we denote by <math> \mathbb{Z} \langle Ind(Res), Ind^2(Res^2), \cdots, Ind^n(Res^n) \rangle </math>. Using Frobenius reciprocity, we will show that the formal ring for any group <math> G_n </math> is in fact a commutative polynomial ring of 1 variable. If time allows, we will also show that for a sequence of symmetric groups <math> S_n \supset S_{n-1} \supset \cdots \supset S_2 \supset S_1 = \{1\} </math>, the formal ring of <math> S_n </math> isomorphic to a polynomial ring <math> \mathbb{Z}[x]/(f(x)) </math>, where <math>f(x)</math> is a polynomial of degree <math> n </math>.<br />
<br />
=== November 7, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 14, Soumya Sankar ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 21, Cancelled due to Thanksgiving===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== November 28, Niudun Wang ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== December 5, Patrick Nicodemus ===<br />
<br />
Title: Applications of Algorithmic Randomness and Complexity<br />
Abstract: I will introduce the fascinating field of Kolmogorov Complexity and point out its applications in such varied areas as combinatorics, statistical inference and mathematical logic. In fact the Prime Number theorem, machine learning and Godel's Incompleteness theorem can all be investigated fruitfully through a wonderful common lens.<br />
<br />
=== December 12, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Spark483https://wiki.math.wisc.edu/index.php?title=Madison_Math_Circle&diff=15997Madison Math Circle2018-09-17T04:51:01Z<p>Spark483: /* Meetings for Fall 2018 */</p>
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For the site in Spanish, visit [[Math Circle de Madison]]<br />
=What is a Math Circle?=<br />
The Madison Math Circle is a weekly series of mathematically based activities aimed at interested middle school and high school students. It is an outreach program organized by the UW Math Department. Our goal is to provide a taste of exciting ideas in math and science. In the past we've had talks about plasma and weather in outer space, video game graphics, and encryption. In the sessions, students (and parents) are often asked to explore problems on their own, with the presenter facilitating a discussion. The talks are independent of one another, so new students are welcome at any point.<br />
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The level of the audience varies quite widely, including a mix of middle school and high school students, and the speakers generally address this by considering subjects that will be interesting for a wide range of students.<br />
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[[Image: MathCircle_2.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <br />
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After each talk we'll have pizza provided by the Mathematics Department, and students will have an opportunity to mingle and chat with the speaker and with other participants, to ask questions about some of the topics that have been discussed, and also about college, careers in science, etc.<br />
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'''The Madison Math circle was featured in Wisconsin State Journal:''' [http://host.madison.com/wsj/news/local/education/local_schools/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.html check it out]!<br />
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=All right, I want to come!=<br />
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We have a weekly meeting, <b>Monday at 6pm in 3255 Helen C White Library</b>, during the school year. <b>New students are welcome at any point! </b> There is no fee and the talks are independent of one another, so you can just show up any week, but we ask all participants to take a moment to register by following the link below:<br />
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[https://uwmadison.co1.qualtrics.com/jfe/form/SV_e9WdAs2SXNurWFD '''Math Circle Registration Form''']<br />
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All of your information is kept private, and is only used by the Madison Math Circle organizer to help run the Circle. <br />
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If you are a student, we hope you will tell other interested students about these talks, and speak with your parents or with your teacher about organizing a car pool to the UW campus. If you are a parent or a teacher, we hope you'll tell your students about these talks and organize a car pool to the UW (all talks take place in 3255 Helen C White Library, on the UW-Madison campus, right next to the Memorial Union).<br />
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==Directions and parking==<br />
Our meetings are held on the 3rd floor of Helen C. White Hall in room 3255.<br />
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[[File: Helencwhitemap.png|400px]]</div><br />
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'''Parking.''' Parking on campus is rather limited. Here is as list of some options:<br />
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*There is a parking garage in the basement of Helen C. White, with an hourly rate. Enter from Park Street.<br />
*A 0.5 mile walk to Helen C. White Hall via [http://goo.gl/cxTzJY these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/Gkx1C in Lot 26 along Observatory Drive].<br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/vs17X in Lot 34]. <br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], 2 metered spots (25 minute max) [http://goo.gl/maps/ukTcu in front of Lathrop Hall].<br />
*A 0.2 mile walk to Helen C. White Hall via [http://goo.gl/b8pdk2 these directions] 6 metered spots (25 minute max) around [http://goo.gl/maps/6EAnc the loop in front of Chadbourne Hall] .<br />
*For more information, see the [http://transportation.wisc.edu/parking/parking.aspx UW-Madison Parking Info website].<br />
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==Email list==<br />
The best way to keep up to date with the what is going is by signing up for our email list. Send an empty email to join-mathcircle@lists.wisc.edu<br />
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==Contact the organizers==<br />
The Madison Math Circle is organized by a group of professors and graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. If you have any questions, suggestions for topics, or so on, just email the '''organizers''' [mailto:mathcircleorganizers@lists.wisc.edu here]. We are always interested in feedback!<br />
<center><br />
<gallery widths=480px heights=240px mode="packed"><br />
File:de.jpg|[https://www.math.wisc.edu/~derman/ Prof. Daniel Erman]<br />
File:Betsy.jpg|[http://www.math.wisc.edu/~stovall/ Prof. Betsy Stovall]<br />
</gallery><br />
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<gallery widths=500px heights=250px mode="packed"><br />
File:juliettebruce.jpg|[http://www.math.wisc.edu/~juliettebruce/ Juliette Bruce]<br />
File:Ee.jpg|[http://www.math.wisc.edu/~evaelduque/ Eva Elduque]<br />
File:mrjulian.jpg|[http://www.math.wisc.edu/~mrjulian/ Ryan Julian]<br />
File:soumyasankar.jpg|[http://www.math.wisc.edu/~soumyasankar Soumya Sankar]<br />
</gallery><br />
</center><br />
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==Donations==<br />
Please consider donating to the Madison Math Circle. As noted in our [https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf annual report], our main costs consist of pizza and occasional supplies for the speakers. So far our costs have been covered by donations from the UW Mathematics Department as well as a generous gifts from a private donor. But our costs are rising, primarily because this year we expect to hold more meetings than in any previous year. In fact, this year, we expect to spend at least $2500 on pizza and supplies alone.<br />
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So please consider donating to support your math circle! The easiest way to donate is to go to the link:<br />
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[http://www.math.wisc.edu/donate Online Donation Link]<br />
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There are instructions on that page for donating to the Math Department. <b> Be sure and add a Gift Note saying that the donation is intended for the "Madison Math Circle"!</b> The money goes into the Mathematics Department Annual Fund and is routed through the University of Wisconsin Foundation, which is convenient for record-keeping, etc.<br />
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Alternately, you can bring a check to one of the Math Circle Meetings. If you write a check, be sure to make it payable to the "WFAA" and add the note "Math Circle Donation" on the check. <br />
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Or you can just pay in cash, and we'll give you a receipt.<br />
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==Help us grow!==<br />
If you like Math Circle, please help us continue to grow! Students, parents, and teachers can help by:<br />
*Posting our [https://www.math.wisc.edu/wiki/images/MMC_Flyer_2016.pdf '''flyer'''] at schools or anywhere that might have interested students<br />
*Discussing the Math Circle with students, parents, teachers, administrators, and others<br />
*Making an announcement about Math Circle at PTO meetings<br />
*Donating to Math Circle<br />
Contact the organizers if you have questions or your own ideas about how to help out.<br />
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=Meetings for Fall 2018=<br />
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<center><br />
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Unless specified talks start at '''6pm in room 3255 of Helen C. White Library''', unless otherwise noted.<br />
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{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2018<br />
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! Date !! Speaker !! Topic<br />
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| September 17, 2018 || Sun Woo Park || Why are Donuts and Cream Puffs "different"?<br />
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| September 24, 2018 || Ben Bruce || Three Cottages Problem<br />
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| October 1, 2018 || Kit Newton || How to calculate Pi if all you can do is throw things<br />
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| October 8, 2018 || Connor Simpson || TBD<br />
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| October 15, 2018 || TBD || TBD<br />
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| October 22, 2018 || TBD || TBD<br />
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| October 29, 2018 || TBD || TBD<br />
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| November 5, 2018 || Christian Geske || Josephus Problem<br />
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| November 12, 2018 || TBD || TBD<br />
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| November 19, 2018 || TBD || TBD<br />
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|}<br />
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</center><br />
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=Off-Site Meetings=<br />
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We will hold some Math Circle meetings at local high schools on early release days. Our schedule for 2018-2019has not yet been determined. If you are interesting in having us come to your high school, please contact us!<br />
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<!--<br />
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{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Fall 2017<br />
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! Date !! Time !! Location !! Speaker !! Topic <br />
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| October 2nd || 2:45pm|| East High School - Madison, WI || [http://www.math.wisc.edu/~moises/ Moisés Herradón] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_2_2017_.28East_High_School.29 How to make it as a Hackenbush player in the planet Zubenelgenubi 4] <br />
|-<br />
| November 2nd || 9:30am || Wisconsin Institute for Discovery - Madison, WI || [http://www.math.wisc.edu/~rzachariah/ Alisha Zachariah] || <br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_2_2017_.28WID.29_-_1 Fractals, Fractions and Fibonnaci.]<br />
|-<br />
| November 2nd (Canceled) || 11:00am || Wisconsin Institute for Discovery - Madison, WI || [http://zachcharles.wordpress.com Zach Charles] || <br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_2_2017_.28WID.29_-_2 1+1 = 10 or "How does my computer do anything?"]<br />
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| November 2nd || 6:00pm || Whitewater High School - Whitewater, WI || [http://www.math.wisc.edu/~juliettebruce Juliette Bruce] || <br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_2_2017_.28Whitewater.29 Doodling Daydreams]<br />
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| November 3rd || 10:30am || KM Global - Wales, WI || [http://www.math.wisc.edu/~stovall/ Betsy Stovall] ||<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_3_2017_.28KM_Global.29 Recent discoveries in mathematics]<br />
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| November 27th || 2:45pm|| JMM High School - Madison, WI || [http://www.math.wisc.edu/~juliettebruce Juliette Bruce] || <br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_27_2017_.28JMM_High_School.29 Is any knot not the unknot?]<br />
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| December 11th || 2:45pm|| East High School - Madison, WI || [https://sites.google.com/wisc.edu/jwg John Wiltshire-Gordon] ||<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_11_2017_.28East_High_School.29 What if seven is zero?]<br />
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! colspan="5" style="background: #e8b2b2;" align="center" | Spring 2018<br />
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! Date !! Time !! Location !! Speaker !! Topic <br />
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| February 19th || 2:45pm|| East High School - Madison, WI || Jordan Ellenberg || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_19_2018_.28East_High_School.29 Is math destroying the right to vote?] <br />
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| March 1st || 9:30am || Wisconsin Institute for Discovery - Madison, WI || Wanlin Li || <br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_1_2018_.28WID.29_-_1 From Patterns to Functions?]<br />
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| March 1st || 10:45am || Wisconsin Institute for Discovery - Madison, WI || Daniel Erman || <br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_1_2018_.28WID.29_-_2 What does math research look like?]<br />
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| March 5th || 2:45pm|| JMM High School - Madison, WI || Zach Charles || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_5_2018_.28JMM_High_School.29 1+1 = 10 or "How does my computer do anything?"]<br />
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| March 19th || 2:45pm|| East High School - Madison, WI || Phil Wood || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_19_2018_.28East_High_School.29 The Mathematics of Winning Strategies ] <br />
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| April 30th || 2:45pm|| JMM High School - Madison, WI || Juliette Bruce || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#April_30_2018_.28JMM_High_School.29 From Books to Mars]<br />
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|}<br />
</center><br />
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=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
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== Archived Abstracts ==<br />
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[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2016-2017 2016 - 2017 Math Circle Page]<br />
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[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2016-2017 2016 - 2017 Abstracts]<br />
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[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
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[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
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[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 2015 - 2015 Abstracts]<br />
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[[Archived Math Circle Material]]<br />
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==Link for presenters (in progress)==<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations Advice For Math Circle Presenters]<br />
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[http://www.mathcircles.org/content/lesson-plans Sample Lesson Plans]<br />
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[http://www.mathcircles.org/content/circle-box "Circle in a Box"]</div>Spark483