https://wiki.math.wisc.edu/index.php?title=Special:NewPages&feed=atom&hideredirs=1&limit=50&offset=&namespace=0&username=&tagfilter=&size-mode=max&size=0UW-Math Wiki - New pages [en]2024-03-29T12:38:49ZFrom UW-Math WikiMediaWiki 1.39.5https://wiki.math.wisc.edu/index.php/Applied/ACMS/absS24Applied/ACMS/absS242024-03-06T02:17:04Z<p>Qli36: Blanked the page</p>
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<div></div>Qli36https://wiki.math.wisc.edu/index.php/GAPSGAPS2024-02-26T19:50:24Z<p>Abyars: </p>
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<div>The '''Graduate Analysis and PDEs Seminar (GAPS)''' is intended to build community for graduate students in the different subfields of analysis and PDEs. The goal is to give accessible talks about your current research projects, papers you found interesting on the arXiv, or even just a theorem/result that you use and think is really cool!<br />
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We currently meet '''Mondays, 1:20pm-2:10pm, in Van Vleck 901'''. Oreos and apple juice (from concentrate) are provided. If you have any questions, please email the organizers: [https://salhamdani.github.io Summer Al Hamdani] (alhamdani (at) wisc.edu) and [https://sites.google.com/wisc.edu/allisonbyars Allison Byars] (abyars (at) wisc.edu).<br />
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To join the mailing list, send an email to: gaps+subscribe@g-groups.wisc.edu. <br />
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=== Spring 2024 ===<br />
{| class="wikitable"<br />
|+<br />
!Date<br />
!Speaker<br />
!Title<br />
!Comments<br />
|-<br />
|2/26<br />
|Organizational Meeting<br />
|<br />
|<br />
|-<br />
|3/4<br />
|skip-bc of PLANT<br />
|<br />
|<br />
|-<br />
|3/11<br />
|Amelia Stokolosa<br />
|Inverses of product kernels and flag kernels on graded Lie groups<br />
|1:20-1:50<br />
|-<br />
|3/11<br />
|Allison Byars<br />
|Wave Packets for DNLS<br />
|1:55-2:10<br />
|-<br />
|3/18<br />
|Mingfeng Chen<br />
|Nikodym set vs Local smoothing for wave equation<br />
|<br />
|-<br />
|4/1<br />
|Lizhe Wan<br />
|TBD<br />
|<br />
|-<br />
|4/8<br />
|Taylor Tan<br />
|TBD<br />
|<br />
|-<br />
|4/15<br />
|Kaiyi Huang<br />
|TBD<br />
|<br />
|-<br />
|4/22<br />
|Sam Craig<br />
|TBD<br />
|<br />
|-<br />
|4/29<br />
|Allison Byars<br />
|TBD<br />
|<br />
|}<br />
<br />
==== Spring 2024 Abstracts ====<br />
<br />
===== '''[https://sites.google.com/wisc.edu/stokolosa/home Amelia Stokolosa]: Inverses of product kernels and flag kernels on graded Lie groups''' =====<br />
'''''Abstract.''''' Consider the following problem solved in the late 80s by Christ and Geller: Let $Tf = f*K$ where $K$ is a homogeneous distribution on a graded Lie group. Suppose $T$ is $L^2$ invertible. Is $T^{-1}$ also a translation-invariant operator given by convolution with a homogeneous kernel? Christ and Geller proved that the answer is yes. Extending the above problem to the multi-parameter setting, consider the operator $Tf = f*K$, where $K$ is a product or a flag kernel on a graded Lie group $G$. Suppose $T$ is $L^2$ invertible. Is $T^{-1}$ also given by group convolution with a product or flag kernel accordingly? We prove that the answer is again yes. In the non-commutative setting, one cannot make use of the Fourier transform to answer this question. Instead, the key construction is an a priori estimate.<br />
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===== '''[https://sites.google.com/wisc.edu/allisonbyars Allison Byars]: Wave Packets for DNLS''' =====<br />
'''''Abstract.''''' Well-posedness for the derivative nonlinear Schrödinger equation (DNLS) was recently proved by Harrop-Griffiths, Killip, Ntekoume, and Vișan. The next natural question to ask is, "what does the solution look like?", i.e. does it disperse in time at a rate similar to the linear solution? In 2014, Ifrim and Tataru introduced the method of wave packets in order to prove a dispersive decay estimate for NLS. The idea of wave packets is to find an approximate solution to the equation which is localized in both space and frequency, and use this to prove an estimate on the nonlinear solution. In this talk, we will explore how this method can be applied to the DNLS equation. <br />
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===== '''[https://sites.google.com/view/chenmingfeng/home Mingfeng Chen]: Nikodym set vs Local smoothing for wave equation''' =====<br />
'''''Abstract.''''' This talk is about classifying maximal average over planar curves. It is well-known that if we consider the maximal operator defined by averaging over planar line, then the maximal operator is not bounded on $L^p(\mathbb{R}^2)$ for any $p<\infty$ because of the existence of Nikodym set. On the other hand, if we replace line by parabola or circle, the celebrated Bourgain's circular maximal theorem shows that such operator is bounded for every $p>2$. We classify all the maximal operator, that is: we find all the curves such that Nikodym sets exist, thus the corresponding maximal operator is not bounded on $L^p$ for any $p<\infty$; for other curves, we prove sharp $L^p$ bound for the maximal operator.<br />
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===== '''[https://sites.google.com/wisc.edu/lizhewan/ Lizhe Wan]: TBD''' =====<br />
'''''Abstract.'''''<br />
<br />
===== '''Taylor Tan: TBD''' =====<br />
'''''Abstract.'''''<br />
<br />
===== '''Kaiyi Huang: TBD''' =====<br />
'''''Abstract.'''''<br />
<br />
===== '''[https://people.math.wisc.edu/~secraig2/ Sam Craig]: TBD''' =====<br />
'''''Abstract.'''''<br />
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===== '''[https://sites.google.com/wisc.edu/allisonbyars Allison Byars]: TBD''' =====<br />
'''''Abstract.'''''</div>Alhamdanihttps://wiki.math.wisc.edu/index.php/Colloquia/Spring_2025Colloquia/Spring 20252024-02-26T17:12:31Z<p>Cuyanik: </p>
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<div>{| cellpadding="8"<br />
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|April 22,24,25<br />
|Mladen Bestvina (Utah) <br />
|[[# TBA| '''Distinguished Lecture Series''']]<br />
|Uyanik<br />
|<br />
|}<br />
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==Abstracts==<br />
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===<DATE>: <PERSON> (INSTITUTION)===<br />
Title: <TITLE><br />
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Abstract: <ABSTRACT></div>Sjziemenhttps://wiki.math.wisc.edu/index.php/Colloquia/Fall_2024Colloquia/Fall 20242024-02-26T17:12:14Z<p>Mfeldman2: </p>
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|Nov 1<br />
| reserved <br />
|[[# TBA| TBA ]]<br />
| Feldman, Tran<br />
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== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT></div>Sjziemenhttps://wiki.math.wisc.edu/index.php/Madison_Math_Circle_Abstracts_2023-2024Madison Math Circle Abstracts 2023-20242024-02-14T15:15:24Z<p>Uandrews2: Created page with "== Abstract 10/2 == <center> {| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20" |- | bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews''' |- | bgcolor="#BDBDBD" align="center" | '''Title: How many paradoxes are there?''' |- | bgcolor="#BDBDBD" | "This statement is false". That's the so-called liar's paradox. (Think through why that statement cannot be either true or false). A paradox is a sta..."</p>
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<div>== Abstract 10/2 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: How many paradoxes are there?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
"This statement is false". That's the so-called liar's paradox. (Think through why that statement cannot be either true or false). A paradox is a statement or collection of statements that cannot be meaningfully assigned truth values. Aristotle thought that all paradoxes were essentially the same as the liar's paradox. In 1985, Yablo found a different paradox (though there is some disagreement here). A brand new paper claimed to show that there are only 2 paradoxes (Yablo and the liar's paradox). I'll talk about all these topics and also a brand new paradox. Are there more than 2 paradoxes after all?<br />
|} <br />
</center><br />
<br />
== Abstract 10/16 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Diego Rojas La Luz'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: How to Not Die While Eating a Poisoned Chocolate Bar'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
We are going to talk about Chomp, a game where you take turns eating chocolate and you try not to die from poisoning! This is one of those very easy-to-state combinatoric games which happens to be very hard to fully analyze. We'll see that we can say some rather surprising things regarding winning strategies, so stay tuned for that. Who wants to play?<br />
|} <br />
</center><br />
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== Abstract 10/30 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Oh Hoon Kwon'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Your (Life) Turning Points: Chasing Angles for Proofs'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
We're bringing a fresh approach to Euclidean geometry by incorporating physical movements involving a pencil to illustrate proofs related to angle concepts. This inventive method acts as a potential link between inductive, exploratory techniques and deductive proofs. It provides students with a new perspective on Euclidean geometry, particularly in the context of angle concepts, making it an enjoyable and captivating way to engage with the subject.<br />
|} <br />
</center><br />
<br />
== Abstract 11/13 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Aleksandra Cecylia Sobieska'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Trapezoid Numbers'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Perfect squares are numbers that can be represented as a square arrangement of dots, like 1, 4, 9, 16, and so on. This Math Circle, we will investigate a similar question: what numbers can be represented as a trapezoidal arrangement of dots?<br />
|} <br />
</center></div>Uandrews2https://wiki.math.wisc.edu/index.php/Directed_Reading_Program_Spring_2024Directed Reading Program Spring 20242024-02-05T19:44:51Z<p>Drp: /* Requirements */ Updated final presentation date</p>
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<div>'''What is it?''' The Directed Reading Program (DRP) in the UW Madison Department of Mathematics pairs undergraduate students with graduate mentors for semester-long independent studies. During the semester, the student will work through a mathematical text and meet weekly to discuss it with their mentor. The original DRP was started by graduate students at the University of Chicago over a decade ago, and has had immense success. It has since spread to many other math departments who are members of the [https://sites.google.com/view/drp-network/ DRP Network.]<br />
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'''Why be a student?''' <br />
*Learn about exciting math from outside the mainstream curriculum!<br />
* Prepare for future reading and research, including REUs!<br />
*Meet other students interested in math!<br />
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'''Why be a mentor?'''<br />
*Practice your mentorship skills!<br />
*It strengthens our math community!<br />
*Solidify your knowledge in a subject!<br />
'''Current Organizers:''' Ivan Aidun, Allison Byars, Jake Fiedler, John Spoerl<br />
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===Requirements===<br />
At least one hour per week spent in a mentor/mentee setting. Students spend about two hours a week on individual study, outside of mentor/mentee meetings. At the end, students give a 10-12 minute presentation at the end of the semester introducing their topic. This semester, it is scheduled for '''Wednesday, April 24th.'''<br />
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=== Applications ===<br />
Check out our [https://wiki.math.wisc.edu/index.php/Directed_Reading_Program#Past_Semesters main page for examples of past projects].<br />
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'''Students:''' https://docs.google.com/forms/d/e/1FAIpQLSf2lm8Geuc6jwznBgGP5JjSJZuMITOw252e9qPOZCEQuFGIQw/viewform <br />
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'''Mentors:''' Applications are closed.<br />
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===Questions?===<br />
Contact us at drp-organizers@g-groups.wisc.edu<br />
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== Projects ==<br />
{| class="wikitable"<br />
|+Spring 2024 Projects<br />
!Title<br />
!Abstract<br />
!Required Background<br />
|-<br />
|Polynomial Methods<br />
|We will read Larry Guth’s book Polynomial Methods in Combinatorics and maybe some related short papers to understand how polynomials and their properties are applied to combinatorics, incidence geometry and harmonic analysis.<br />
|The material is accessible to students with linear algebra background. Corequisite of MATH 542 and 522 is recommended.<br />
|-<br />
|Algebraic Geometry<br />
|This project introduces scheme theory, a fundamental part of modern algebraic geometry, from a geometrically focused point of view. Topics to be covered will include affine schemes and their topology, an introduction to sheaves, structure sheaves, general schemes, and some examples. We will use Eisenbud and Harris' "The Geometry of Schemes."<br />
|The only strictly necessary requirement is familiarity with basic point set topology and commutative algebra at the level of a one-semester course. Rings, ideals, modules, localization, tensor products, etc. Basic algebraic geometry can be introduced at the beginning, but it would help to know about affine varieties, affine coordinate rings, and the correspondence between them.<br />
|-<br />
|Analysis<br />
|We will read Polynomial Methods in Combinatorics by Larry Guth. This covers a variety of applications of polynomials to different fields in mathematics, including combinatorics, analysis, and geometry. While I am most interested in analysis, we can choose what among the applications in the book interest you and focus on that.<br />
|Linear algebra, MATH 521-22.<br />
|-<br />
|Algebra/Probability<br />
|Free probability is a field which attempts to apply ideas from probability to more abstract settings, especially where the variables don't commute. In these settings we might not even be able to talk about 'probabilities', but thinking about expectations and distributions (suitably translated) can still tell us a lot. For example, it can tell us what the eigenvalues of a random matrix look like. Some funny things happen in the translation, like the role of the bell curve being taken by the semicircle (see Wigner's Semicircle Law for a related result).<br />
<br />
The material involves an interplay between things like operator algebras, combinatorics and probability, and would be interesting mostly to students who enjoy probability and didn't mind taking abstract algebra.<br />
|Students should be comfortable with linear algebra and have taken some abstract algebra (341, 541, and maybe 540 would be good). Some background in probability (not necessarily measure-theoretic) would help provide context. The material in the book doesn't require much heavy theory, so it should be possible to fill in any blanks along the way.<br />
|-<br />
|Real Analysis<br />
|Wavelets are a fun topic if you're interested in learning about a very useful application of both real analysis and linear algebra! They are used in lots of different areas of engineering (e.g. signal processing) and are interesting in their own right as a pure math tool! If you are interested in learning a more advanced topic of math, sign up for this DRP!<br />
|Real analysis (Math 521) and linear algebra (math 341 or 540) are prerequisites. If you have studied, Fourier series that's a plus but not a prerequisite! If you are motivated to learn something new, don't hesitate to sign up! We're all here to learn so questions are always and will always be welcome! I'm planning on using "An introduction to wavelets through linear algebra" by Michael Frazier.<br />
|-<br />
|History of Mathematics<br />
|We will read and discuss sections from John Stillwell's Mathematics and Its History. Which particular sections we read can be selected by any students in the group based on their interests. Our goal is to gain an appreciation for some of how mathematics became what it is today. What problems motivated its development, and how do our modern conceptions of things align (or not!) with what mathematicians were doing historically? What can we learn for doing math and other kinds of problem solving in the present?<br />
|We think interested students should have taken at least one proof-based math course. We think this project is unique in that it can accommodate students of widely varying pre-existing mathematical knowledge. Having little math knowledge means this project can give you perspective and intuition for math you will learn as you progress through the curriculum. Having a lot of math knowledge means this project can help you see the "big picture" of how facts you have learned connect to each other, sometimes in surprising ways.<br />
|-<br />
|Dynamical Systems (Reaction Networks)<br />
|Ever since Edward Lorenz found chaos emerging from his simple meteorological model, we have noticed that it is quite hard to try to understand the behavior of even very simple non-linear systems of differential equations. But these systems show up time and time again in nature, with a variety of very particular non-chaotic dynamics that we can make sense of. The study of Reaction Networks surprisingly manages to identify and classify these dynamics in systems that are very common in nature; from the enzymatic reactions on cells, to epidemiological models and even ecological population models. Using simple graph theory and linear algebra, we can uncover amazing results for the dynamics of these types of systems by abstracting some ideas. We will follow Martin Feinberg's book "Foundations of Chemical Reaction Network Theory".<br />
<br />
My goal in this DRP is to showcase this beautiful field of mathematics that lies in the intersection of both Pure and Applied Math, showing that these are more related that they usually seem, and how with abstraction and math we can uncover deeper truths about the structure of nature.<br />
|Students should be familiar with the language of elementary qualitative theory of ordinary differential equations (e. g., the meaning of asymptotic stability), good knowledge of modern linear algebra and calculus. For differential equations, Math 415 or Math 519 will suffice. For linear algebra, any course which dictates it is good enough.<br />
|-<br />
|Linear Representations of Finite Groups<br />
|We’ll be reading Serre’s Linear Representation of Finite Groups. <br />
|Abstract Algebra (Math 541) is expected. I expect the student to be somewhat independent due to time.<br />
|-<br />
|Geometric Measure Theory<br />
|Starting from the basics, the goal is to cover a solid amount of geometric measure theory, which is a field used to understand the geometry of complicated (but common in the real world) sets. We'll begin by discussing measures, and move into rectifiable curves/sets. We'll also talk about how projections affect the geometry of sets, in particular purely unrectifiable sets. Then, I hope to get into other topics like weak tangents and Plateau's problem generalized beyond smooth curves.<br />
|Students should have taken 521. Additional experience in proof-based math courses, especially analysis classes, will be very helpful. Students don't necessarily need to have seen measure theory, but it wouldn't hurt.<br />
|-<br />
|Abstract Algebra<br />
|We plan to follow the book Ideals, Varieties, and Algorithms by Cox-Little-O'Shea, roughly aiming to cover the first two chapters. This means we'll explore the relationship between algebraic objects (like polynomials) and geometric objects (like curves). We'll read about an important computational tool called Gröbner bases, which are used to find solutions to systems of polynomial equations (motivated by methods from linear algebra). This project, and the book we've chosen, will assume no prior knowledge of abstract algebra, and we'll learn any necessary concepts along the way! If you like a mix of theory and explicit examples, this project is for you!<br />
|This project is intended for students who have taken linear algebra and are interested in abstract algebra, but don't have much (or any) background in abstract algebra.<br />
|}<br />
<br />
== Presentation Schedule ==<br />
TBA</div>Aidunhttps://wiki.math.wisc.edu/index.php/SIAM_Fall_2023SIAM Fall 20232024-01-29T20:21:12Z<p>Sjziemen: Created page with "== Fall2023 == {| class="wikitable" |+ !Date !Location !Speaker !Title |- |9/29 |Zoom and VV911 |Solly Parenti (JPMorgan Chase & Co.) |What is ... a software engineering interview? |- |10/13 |Zoom and VV911 |Xiaopeng Li (Columbia University) |Convergence of the Momentum Method for Semi-Algebraic Functions with Locally Lipschitz Gradients |- |10/20 |VV911 |Yingxin Zhao (UBS Investment Bank) |Industry talk from UBS quant |- |10/27 |Zoom and VV911 |Evan Sorensen (Columbia U..."</p>
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<div>== Fall2023 ==<br />
{| class="wikitable"<br />
|+<br />
!Date<br />
!Location<br />
!Speaker<br />
!Title<br />
|-<br />
|9/29<br />
|Zoom and VV911<br />
|Solly Parenti (JPMorgan Chase & Co.)<br />
|What is ... a software engineering interview?<br />
|-<br />
|10/13<br />
|Zoom and VV911<br />
|Xiaopeng Li (Columbia University)<br />
|Convergence of the Momentum Method for Semi-Algebraic Functions with Locally Lipschitz Gradients<br />
|-<br />
|10/20<br />
|VV911<br />
|Yingxin Zhao (UBS Investment Bank)<br />
|Industry talk from UBS quant<br />
|-<br />
|10/27<br />
|Zoom and VV911<br />
|Evan Sorensen (Columbia University)<br />
|Applying for postdocs: it’s not just about how many papers you have<br />
|-<br />
|11/10<br />
|VV911<br />
|Jiayin Lu (Harvard University)<br />
|Computational geometry: Voronoi tessellation, Delaunay triangulation, and their fun applications<br />
|-<br />
|11/17<br />
|Zoom and VV911<br />
|Wyliena Guan (University of North Carolina Chapel Hill)<br />
|A Pharma Industry Overview from a PhD Student’s Perspective<br />
|-<br />
|12/08<br />
|VV911<br />
|Will Hardt (University of Wisconsin, Madison & Federal Reserve)<br />
|My Journey into Quantitative Finance<br />
|}<br />
<br />
==Abstracts==<br />
<br />
'''September 29, Solly Parenti (JPMorgan Chase & Co.):''' I'll share my experiences going through a bunch of software engineering interviews, as well as how I learned how to program and my thoughts on industry jobs.<br />
<br />
'''October 13, Xiaopeng Li (Columbia University):''' We propose a new length formula that governs the iterates of the momentum method when minimizing differentiable semi-algebraic functions with locally Lipschitz gradients. It enables us to establish local convergence, global convergence, and convergence to local minimizers without assuming global Lipschitz continuity of the gradient, coercivity, and a global growth condition, as is done in the literature. As a result, we provide the first convergence guarantee of the momentum method starting from arbitrary initial points when applied to principal component analysis, matrix sensing, and linear neural networks.<br />
<br />
'''October 20, Yingxin Zhao (UBS Investment Bank):'''In this talk, I will give an overview of the different job roles at Investment Banking, share my career path as an interest rate quant starting from graduate program to Executive Director over the past 12 years at UBS and give a few tips on quant job interviews. At the end of the seminar, I am happy to take printed copies of your CVs and email back my review feedback later.<br />
<br />
'''October 27, Evan Sorensen (Columbia University):''' When applying for postdocs, I’ve often heard that nothing is more important than your research. While there is much truth to this, I have found that being a successful candidate takes so much more than just producing quality research. I will talk about lessons learned from applying to research-focused postdocs and give practical advice for how to increase your visibility and status in the community. This talk will address both people on the job market now as well as those planning to apply in future years.<br />
<br />
'''November 10, Jiayin Lu (Harvard University):''' I will discuss some computational geometry work related to Voronoi tessellation and Delaunay triangulation. Voronoi tessellation is a beautiful and simple mathematical concept. Given a set of discrete points in space, locations in the space are associated with the closest point in the point set. <br />
<br />
It has important applications in science and engineering. Material scientists can generate Voronoi diagrams on atomistic systems, and analyze the Voronoi cell geometries to study material properties and predict material failure. However, as systems grow in size (e.g. millions of particles), the computational demands increase, necessitating efficient and scalable computational solutions. I will discuss our recent work on the multithreaded parallel computation of the Voronoi diagrams. <br />
<br />
A closely related geometry concept is the Delaunay triangulation, which is the duality graph of Voronoi tessellation. It can be constructed by connecting points sharing Voronoi cell walls. It can be used for geometry meshing, which has applications in computer graphics and numerical simulations using the finite element method. I will discuss our recent work on multithreaded geometry meshing in 2D. <br />
<br />
Lastly, I will show some other fun applications of these geometry concepts: (1) The generation of insect wing patterns, and (2) Making colorful, mosaic style art. <br />
<br />
'''November 17, Wyliena Guan (University of North Carolina Chapel Hill):''' The pharmaceutical industry is one of the most important and dynamic industries in the world, responsible for developing and delivering life-saving and life-changing medicines to patients around the globe. But what is it really like to work in the pharma industry? How does it differ from working in academia or other industries? <br />
<br />
In this talk, Lina will share her insights from their internship at AbbVie and her conversations with friends in pharma. She will discuss the different career paths available in the industry, the challenges and rewards of working in pharma, and what it takes to be successful in this field. <br />
<br />
'''December 08, Will Hardt ((University of Wisconsin, Madison & Federal Reserve):''' I will share my experience so far in quantitative finance, which consists of internships in trading and data science and — soon — a job at the Federal Reserve. I’ll discuss what drew me into the field, the application processes, and the work itself.</div>Sjziemenhttps://wiki.math.wisc.edu/index.php/Applied/Physical_Applied_Math/Fall2023Applied/Physical Applied Math/Fall20232024-01-17T19:43:57Z<p>Spagnolie: /* Fall 2023 */</p>
<hr />
<div>== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 13<br />
|Yue Sun<br />
|Current research<br />
|-<br />
|Sept. 20<br />
|Hanzhang Mao<br />
|Current research<br />
|-<br />
|Sept. 27<br />
|Tom Chandler<br />
|Rectified rotational dynamics of mobile inclusions in two-dimensional active nematics. Ray, Zhang and Dogic, PRL 2023.<br />
|-<br />
|Oct. 4<br />
|Jingyi Li<br />
|Roll cells and disclinations in sheared nematic polymers. Feng, Tao and Leal, JFM 2001.<br />
|-<br />
|Oct. 11<br />
|Madelyn Leembruggen<br />
|<br />
|-<br />
|Oct. 25<br />
|Jiayin Lu & Danyun He<br />
|Wing analysis project at the Field Museum<br />
|-<br />
|Nov. 15<br />
|DFD practice talks<br />
|Talks by Yue Sun, Danyun He, Michael Emanuel, ...<br />
|-<br />
|}</div>Spagnoliehttps://wiki.math.wisc.edu/index.php/Colloquia/Fall_2023Colloquia/Fall 20232024-01-16T15:06:15Z<p>Sjziemen: Created page with "==Fall 2023== {| cellpadding="8" !align="left" | date !align="left" | speaker !align="left" | title !align="left" | host(s) | |- |Sept 8 |[https://www.uwlax.edu/profile/tdas/ Tushar Das] (University of Wisconsin-La Crosse) |Playing games on fractals: Dynamical & Diophantine | Playing games on fractals: Dynamical & Diophantine |Stovall |- |Sept 15 |[https://math.yale.edu/people/john-schotland John Schotland] (Yale) |Nonlocal PDEs and Quantum Optics |Li |- |Sept 22 |[..."</p>
<hr />
<div>==Fall 2023==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Sept 8<br />
|[https://www.uwlax.edu/profile/tdas/ Tushar Das] (University of Wisconsin-La Crosse)<br />
|Playing games on fractals: Dynamical & Diophantine | Playing games on fractals: Dynamical & Diophantine<br />
|Stovall<br />
|-<br />
|Sept 15<br />
|[https://math.yale.edu/people/john-schotland John Schotland] (Yale)<br />
|Nonlocal PDEs and Quantum Optics<br />
|Li<br />
|-<br />
|Sept 22<br />
|[https://www.dumas.io/ David Dumas](University of Illinois Chicago)<br />
|Geometry of surface group homomorphisms<br />
|Zimmer<br />
|-<br />
|Sept 29<br />
|''no colloquium (see Monday)''<br />
|<br />
|<br />
|-<br />
|<b>Monday Oct 2 at 4 pm</b><br />
|[https://www.math.tamu.edu/~titi/ Edriss Titi] (Texas A&M University)<br />
|Distinguished lectures: On the Solvability of the Navier-Stokes and Euler Equations, where do we stand?<br />
|Smith, Stechmann<br />
|-<br />
|Oct 13<br />
|Autumn Kent<br />
|The 0π Theorem<br />
|<br />
|-<br />
|Oct 20<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Some new results in Higher Teichmüller Theory<br />
|Dymarz, Uyanik, GmMaW<br />
|-<br />
|<b>Wednesday Oct 25 at 4 pm</b><br />
|[https://math.mit.edu/~gigliola/ Gigliola Staffilani] (MIT)<br />
|The Schrödinger equations as inspiration of beautiful mathematics<br />
|Ifrim, Smith<br />
|-<br />
|Oct 27<br />
|[https://www.math.purdue.edu/people/bio/banuelos/home Rodrigo Bañuelos] (Purdue)<br />
|Probabilistic tools in discrete harmonic analysis<br />
|Stovall<br />
|-<br />
|<b>Tuesday Oct 31 at 4 pm</b><br />
|[https://www.wisdom.weizmann.ac.il/~dinuri/ Irit Dinur] (The Weizmann Institute of Science)<br />
|<s>Distinguished lectures</s> Cancelled<br />
|Gurevich<br />
|-<br />
|<b>Wednesday Nov 1 at 4 pm</b><br />
|[https://www.wisdom.weizmann.ac.il/~dinuri/ Irit Dinur] (The Weizmann Institute of Science)<br />
|<s>Distinguished lectures</s> Cancelled<br />
|Gurevich<br />
|-<br />
|<b>Tuesday Nov 14 at 4 pm (Stirling 1310)</b><br />
|[https://www.iazd.uni-hannover.de/en/gao Ziyang Gao] (Leibniz University Hannover)<br />
|[[#Gao|Sparsity of rational and algebraic points]]<br />
|Arinkin, Yang<br />
|-<br />
|<b>Monday Nov 20</b><br />
|[https://web.math.princeton.edu/~ruobingz/ Ruobing Zhang] (Princeton)<br />
|[[#Zhang|Metric geometric aspects of Einstein manifolds]]<br />
|Paul<br />
|-<br />
|<b>Monday Nov 27</b><br />
|[https://sites.google.com/uci.edu/yizhezhu Yizhe Zhu] (UC Irvine)<br />
|[[#Zhu|Asymmetry Helps: Non-Backtracking Spectral Methods for Sparse Matrices and Tensors]]<br />
|Shen<br />
|-<br />
|<b>Wednesday Nov 29</b><br />
|[https://u.osu.edu/terry.376/ Caroline Terry] (OSU)<br />
|[[#Terry|Measuring combinatorial complexity via regularity lemmas]]<br />
|Andrews<br />
|-<br />
|<b>Friday Dec 1</b><br />
|[https://math.mit.edu/~dmal/ Dominique Maldague] (MIT)<br />
|[[#Maldague|Sharp square function estimates in Fourier restriction theory]]<br />
|Stovall<br />
|-<br />
|<b>Wednesday Dec 6</b><br />
|[https://rwebber.people.caltech.edu/ Robert Webber] (Caltech)<br />
|[[#Webber|Randomized matrix decompositions for faster scientific computing]]<br />
|Smith<br />
|-<br />
|<b>Monday Dec 11</b><br />
|[https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] (Jagiellonian University, Krakow, Poland)<br />
|[[Colloquia#Fraczyk|Large subgroups in higher rank]]<br />
|Stovall, Zimmer<br />
|}<br />
<br />
==Abstracts==<br />
<br />
<br />
<br />
'''Friday, September 8. Tushar Das'''<br />
<br />
Playing games on fractals: Dynamical & Diophantine<br />
We will present sketches of a program, developed in collaboration with Lior Fishman, David Simmons, and Mariusz Urbanski, which extends the parametric geometry of numbers (initiated by Wolfgang Schmidt and Leonhard Summerer) to Diophantine approximation for systems of m linear forms in n variables. Our variational principle (arXiv:1901.06602) provides a unified framework to compute Hausdorff and packing dimensions of a variety of sets of number-theoretic interest, as well as their dynamical counterparts via the Dani correspondence. Highlights include the introduction of certain combinatorial objects that we call templates, which arise from a dynamical study of Minkowski’s successive minima in the geometry of numbers; as well as a new variant of Schmidt’s game designed to compute the Hausdorff and packing dimensions of any set in a doubling metric space. The talk will be accessible to students and faculty whose interests contain a convex combination of homogeneous dynamics, Diophantine approximation and fractal geometry.<br />
<br />
<br />
'''Friday, September 15. John Schotland'''<br />
<br />
Nonlocal PDEs and Quantum Optics<br />
Quantum optics is the quantum theory of the interaction of light and matter. In this talk, I will describe a real-space formulation of quantum electrodynamics with applications to many body problems. The goal is to understand the transport of nonclassical states of light in random media. In this setting, there is a close relation to kinetic equations for nonlocal PDEs with random coefficients.<br />
<br />
<br />
'''Friday, September 22. David Dumas'''<br />
<br />
The space of homomorphisms from the fundamental group of a compact surface to a Lie group is a remarkably rich and versatile object, playing a key role in mathematical developments spanning disciplines of algebra, analysis, geometry, and mathematical physics. In this talk I will discuss and weave together two threads of research within this larger story: 1) the study of manifolds that are obtained by taking quotients of symmetric spaces (the "inside view") and 2) those obtained as quotients of domains in flag varieties (the "boundary view"). This discussion will start with classical objects--hyperbolic structures on surfaces---and continue into topics of ongoing research.<br />
<br />
<br />
'''Friday, October 13. Autumn Kent'''<br />
<br />
A celebrated theorem of Thurston tells us that among the many ways of filling in cusps of hyperbolic $3$--manfiolds, all but finitely many of them produce hyperbolic manifolds once again. This finiteness may be refined in a number of ways depending on the ``shape’’ of the cusp, and I’ll give a light and breezy discussion of joint work with K. Bromberg and Y. Minsky that allows shapes not covered by any of the previous theorems. This has applications such as answering questions asked in my 2010 job talk here at UW.<br />
<br />
<br />
<br />
''' Friday, October 20. Sara Maloni'''<br />
<br />
The Teichmüller space of a surface S is the space of marked hyperbolic structure on S, up to equivalence. By considering the holonomy representation of such structures, the Teichmüller space can also be seen as a connected component of (conjugacy classes of) representations from the fundamental group of S into PSL(2,R), consisting entirely of discrete and faithful representations. Generalizing this point of view, Higher Teichmüller Theory studies connected components of (conjugacy classes of) representations from the fundamental group of S into more general semisimple Lie groups which consist entirely of discrete and faithful representations.<br />
<br />
We will give a survey of some aspects of Higher Teichmüller Theory and will make links with the recent powerful notion of Anosov representation. We will conclude by focusing on two separate questions: Do these representations correspond to deformation of geometric structures? <br />
Can we generalize the important notion of pleated surfaces to higher rank Lie groups like PSL(d, C)?<br />
The answer to question 1 is joint work with Alessandrini, Tholozan and Wienhard, while the answer to question 2 is joint work with Martone, Mazzoli and Zhang.<br />
<br />
<br />
'''Wednesday, October 25. Gigliola Staffilani'''<br />
<br />
In the last two decades great progress has been made in the study of dispersive and wave equations. Over the years the toolbox used in order to attack highly nontrivial problems related to these equations has developed <br />
to include a collection of techniques: Fourier and harmonic analysis, analytic number theory, math physics, dynamical systems, probability and symplectic geometry. In this talk I will introduce a variety of results using as model problem mainly the periodic 2D cubic nonlinear Schrödinger equation. I will start by giving a physical derivation of the equation from a quantum many-particles system, I will introduce periodic Strichartz estimates along with some remarkable connections to analytic number theory, I will move on the concept of energy transfer and its connection to dynamical systems, and I will end with some results following from viewing the periodic <br />
nonlinear Schrödinger equation as an infinite dimensional Hamiltonian system.<br />
<br />
<br />
'''Friday, October 27. Rodrigo Bañuelos'''<br />
<br />
'''Probabilistic tools in discrete harmonic analysis'''<br />
<br />
The discrete Hilbert transform was introduced by David Hilbert at the beginning of the 20th century as an example of a singular quadratic form. Its boundedness on the space of square summable sequences appeared in H. Weyl’s doctoral dissertation (under Hilbert) in 1908. In 1925, M. Riesz proved that the continuous version of this operator is bounded on L^p(R), 1 < p < \infty, and that the same holds for the discrete version on the integers. Shortly thereafter (1926), E. C. Titchmarsh gave a different proof and from it concluded that the operators have the same p-norm. Unfortunately, Titchmarsh’s argument for equality was incorrect. The question of equality of the norms had been a “simple tantalizing" problem ever since.<br />
<br />
In this general colloquium talk the speaker will discuss a probabilistic construction, based on Doob’s “h-Brownian motion," that leads to sharp inequalities for a collection of discrete operators on the d-dimensional lattice Z^d, d ≥ 1. The case d = 1 verifies equality of the norms for the discrete and continuous Hilbert transforms. The case d > 1 leads to similar questions and conjectures for other Calderón-Zygmund singular integrals in higher dimensions.<br />
<br />
<br />
<div id="Gao">'''Tuesday, November 14. Ziyang Gao'''</div><br />
<br />
'''Sparsity of rational and algebraic points'''<br />
<br />
It is a fundamental question in mathematics to find rational solutions to a given system of polynomials, and in modern language this question translates into finding rational points in algebraic varieties. This question is already very deep for algebraic curves defined over Q. An intrinsic natural number associated with the curve, called its genus, plays an important role in studying the rational points on the curve. In 1983, Faltings proved the famous Mordell Conjecture (proposed in 1922), which asserts that any curve of genus at least 2 has only finitely many rational points. Thus the problem for curves of genus at least 2 can be divided into several grades: finiteness, bound, uniform bound, effectiveness. An answer to each grade requires a better understanding of the distribution of the rational points.<br />
In my talk, I will explain the historical and recent developments of this problem according to the different grades. Another important topic on studying points on curves is the torsion packets. This topic goes beyond rational points. I will also discuss briefly about it in my talk.<br />
<br />
<br />
<div id="Zhang">'''Monday, November 20. Ruobing Zhang'''</div><br />
<br />
'''Metric geometric aspects of Einstein manifolds'''<br />
<br />
Abstract: This lecture concerns the metric Riemannian geometry of Einstein manifolds, which is a central theme in modern differential geometry and is deeply connected to a large variety of fundamental problems in algebraic geometry, geometric topology, analysis of nonlinear PDEs, and mathematical physics. We will exhibit the rich geometric/topological structures of Einstein manifolds and specifically focus on the structure theory of moduli spaces of Einstein metrics.<br />
<br />
My recent works center around the intriguing problems regarding the compactification of the moduli space of Einstein metrics, which tells us how Einstein manifolds can degenerate. Such problems constitute the most challenging part in the metric geometry of Einstein manifolds. We will introduce recent major progress in the field. If time permits, I will propose several important open questions.<br />
<br />
<br />
<div id="Zhu">'''Monday, November 27. Yizhe Zhu'''</div><br />
<br />
'''Asymmetry Helps: Non-Backtracking Spectral Methods for Sparse Matrices and Tensors'''<br />
<br />
The non-backtracking operator, an asymmetric matrix constructed from an undirected graph, connects to various aspects of graph theory, including random walks, graph zeta functions, and expander graphs. It has emerged as a powerful tool for analyzing sparse random graphs, leading to significant advancements with established results for sparse random matrices using this operator. Additionally, algorithms employing the non-backtracking operator have achieved optimal sample complexity in many low-rank estimation problems. In my talk, I will present my recent work utilizing the non-backtracking operator, demonstrating how theoretical elegance drives the design of innovative algorithms through the introduction of asymmetry into data matrices. The discussion will include estimates of the extreme singular values of sparse random matrices and explore data science applications such as hypergraph community detection and tensor completion.<br />
<br />
<br />
<div id="Terry">'''Wednesday, November 29. Caroline Terry'''</div><br />
<br />
'''Measuring combinatorial complexity via regularity lemmas'''<br />
<br />
Many tools have been developed in combinatorics to study global structure in finite graphs. One such tool is called Szemer\'{e}di’s regularity lemma, which gives a structural decomposition for any large finite graph. Beginning with work of Alon-Fischer-Newman, Lov\'{a}sz-Szegedy, and Malliaris-Shelah, it has been shown over the last 15 years that regularity lemmas can be used to detect structural dichotomies in graphs, and that these dichotomies have deep connections to model theory. In this talk, I present extensions of this type of result to arithmetic regularity lemmas, which are analogues of graph regularity lemmas, tailored to the study of combinatorial problems in finite groups. This work uncovered tight connections between tools from additive combinatorics, and ideas from the model theoretic study of infinite groups. <br />
<br />
<br />
<div id="Maldague">'''Friday, December 1. Dominique Maldague''' <br />
<br />
'''Sharp square function estimates in Fourier restriction theory''' <br />
<br />
This talk will provide an overview of recent developments in Fourier restriction theory, which is the study of exponential sums over restricted frequency sets with geometric structure, typically arising in pde or number theory. Decoupling inequalities measure the square root cancellation behavior of these exponential sums. I will highlight recent work which uses the latest tools developed in decoupling theory to prove much more delicate sharp square function estimates for frequencies lying in the cone in R^3 (Guth-Wang-Zhang) and moment curves (t,t^2,...,t^n) in all dimensions (Guth-Maldague). <br />
<br />
<br />
<br />
<div id="Webber">'''Wednesday, December 6. Robert Webber''' <br />
<br />
'''Randomized matrix decompositions for faster scientific computing'''<br />
<br />
Traditional numerical methods based on expensive matrix factorizations struggle with the scale of modern scientific applications. For example, kernel-based algorithms take a data set of size N, form a kernel matrix of size N x N, and then perform an eigendecomposition or inversion at a cost of O(N^3) operations. For data sets of size N >= 10^5, kernel learning is too expensive, straining the limits of personal workstations and even dedicated computing clusters. Randomized iterative methods have emerged as a faster alternative to the classical approaches. These methods combine randomized exploration with information about which matrix structures are important, leading to significant speed gains.<br />
<br />
In this talk, I will review recent developments concerning two randomized algorithms. The first is "randomized block Krylov iteration", which uses an array of random Gaussian test vectors to probe a large data matrix in order to provide a randomized principal component analysis. Remarkably, this approach works well even when the matrix of interest is not low-rank. The second algorithm is "randomly pivoted Cholesky decomposition", which iteratively samples columns from a positive semidefinite matrix using a novelty metric and reconstructs the matrix from the randomly selected columns. Ultimately, both algorithms furnish a randomized approximation of an N x N matrix with a reduced rank k << N, which enables fast inversion or singular value decomposition at a cost of O(N k^2) operations. The speed-up factor from N^3 to N k^2 operations can be 3 million. The newest algorithms achieve this speed-up factor while guaranteeing performance across a broad range of input matrices.<br />
<br />
<br />
<div id="Fraczyk">'''Monday, December 11. Mikolaj Fraczyk''' <br />
<br />
'''Large subgroups in higher rank''' <br />
<br />
Let G be a higher-rank semisimple Lie group (for example, SL_n(R), n > 2). Lattices of G are well understood, thanks to the celebrated Margulis’ arithmeticity theorem. The infinite covolume discrete subgroups of G remain much more mysterious. There has been a lot of progress towards understanding some special classes of subgroups, like the Anosov subgroups, but it is still hard to find "large" discrete subgroups other than the lattices themselves. It is natural to ask if this apparent lack of examples could be explained by new rigidity phenomena. In my talk, I'll make this question more precise and present several instances where the answer is yes, for example, the confined discrete subgroups (j.w. Tsachik Gelander) and the discrete subgroups with finite Bowen-Margulis-Sullivan measure (j.w. Minju Lee).</div>Sjziemenhttps://wiki.math.wisc.edu/index.php/NTSGrad_Spring_2024/AbstractsNTSGrad Spring 2024/Abstracts2024-01-16T14:24:15Z<p>Jhou39: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2024 semester. To go back to the main GNTS page for the semester, click [[NTSGrad_Spring_2024|here.]]<br />
<br />
<br />
== 1/23 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" |[https://sites.google.com/view/tbhatnagar/home?authuser=0 Tejasi Bhatnagar]<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |[[NTSGrad Spring 2024/Abstracts#1/23|Stratification in the moduli space of abelian varieties in char p.]]<br />
|-<br />
| bgcolor="#BCD2EE" |This talk will be an introduction to studying moduli space of abelian varieties in characteristic p via different stratifications. This will be a pre-talk for the upcoming Arizona Winter school in March! I'll try and introduce the theory and give an overview of the kinds of questions and objects we'll come across in the winter school.<br />
|} <br />
</center><br />
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<br><br />
<br />
== 1/30 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" |Joey Yu Luo<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Gross-Zagier formula: motivation<br />
|-<br />
| bgcolor="#BCD2EE" |In this talk, I will sketch how to use the modularity theorem to construct lots of rational points in the elliptic curves, based on the idea of Heegner. Among the constructions, we will see how L-functions come into the story, and how the story end up with the Gross-Zagier formula.<br />
|} <br />
</center><br />
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<br><br />
<br />
== 2/6 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" |'''Hyun Jong Kim'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |A Zoo of L-functions<br />
|-<br />
| bgcolor="#BCD2EE" |I will talk about some different kinds of L-functions (and zeta functions) and maybe some problems surrounding them.<br />
Here are notes: https://github.com/hyunjongkimmath/GNTS_spring_2024_presentation_notes<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== 2/13 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" |Sun Woo Park<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Counting integer solutions of $x^2+y^2=r$ satisfying prime divisibility conditions<br />
|-<br />
| bgcolor="#BCD2EE" |As a slight relation to Hyun Jong's talk on zoos of L-functions last week, we'll explore how one can use Dedekind zeta functions over number fields to count integer points lying on a circle of integral radius r centered at the origin and satisfying some prime divisibility conditions. If time allows, we'll see how this counting problem is related to counting isomorphism classes of elliptic curves over Q of bounded naive heights that admit Q-rational 5-isogenies, an application of which is based on joint work with Santiago Arango-Pineros, Changho Han, and Oana Padurariu.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== 2/20 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" |Eiki Norizuki<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Abelian Varieties over C <br />
|-<br />
| bgcolor="#BCD2EE" | I will talk about the basics of abelian varieties over the complex numbers, in particular their line bundles, polarization and related topics. Time permitting, I may talk about A_g and the Schottky problem.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
==2/27==<br />
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|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |<br />
|-<br />
| bgcolor="#BCD2EE" |<br />
|} <br />
</center><br />
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<br><br />
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==3/5==<br />
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|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" |<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |<br />
|-<br />
| bgcolor="#BCD2EE" |<br />
|} <br />
</center><br />
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<br><br />
<br />
==3/12==<br />
<br />
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{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" |<br />
|-<br />
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<br><br />
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==3/19==<br />
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" |Yifan Wei<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |Periods and Class Field Theory<br />
|-<br />
| bgcolor="#BCD2EE" |We are going to calculate some algebraic integrals on algebraic curves (in particular a twice punctured elliptic curve/Q), figure out their transcendence over Q (to the best of our abilities...). Then we are going to remember class field theory and calculate these integrals cleverly on "the space" (to be revealed in the talk). I'll explain why "the space" is a sane object, and discuss the relation between these integrals and (oh my) Galois representations.<br />
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<br><br />
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==3/26==<br />
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<br><br />
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==4/2==<br />
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==4/9==<br />
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==4/16==<br />
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==4/23==<br />
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<br><br />
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==4/30==<br />
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==5/7==<br />
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<br></div>Jhou39https://wiki.math.wisc.edu/index.php/Group_Actions_and_Dynamics_SeminarGroup Actions and Dynamics Seminar2024-01-11T17:17:45Z<p>Amzimmer2: /* Spring 2024 */</p>
<hr />
<div>During the Spring 2024 semester, '''RTG / Group Actions and Dynamics''' seminar meets in room '''Sterling Hall 3425''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
== Spring 2024 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 22<br />
|[https://sites.google.com/view/aaron-messerla/ Aaron Messerla] (UIC)<br />
|Quasi-isometries of relatively hyperbolic groups with an elementary hierarchy<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|January 24 (1pm in VV 901)<br />
|[https://mitul-islam.github.io/ Mitul Islam] (Max-Planck-Institut)<br />
|Morse-ness in convex projective geometry<br />
|Zimmer<br />
|<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|Rational surface groups on the Hitchin component<br />
|Zimmer<br />
|<br />
|-<br />
|February 5<br />
|[https://www.sayantankhan.io Sayantan Khan] (Michigan)<br />
|Bootstrapping dynamics in the moduli space of non-orientable surfaces<br />
|Uyanik<br />
|<br />
|-<br />
|February 12<br />
|[https://www.noellesawyer.com Noelle Sawyer] (Southwestern)<br />
|Unique Equilibrium States for Geodesic Flows<br />
|Loving, Uyanik, Work<br />
|<br />
|-<br />
|February 19<br />
|[https://web.math.utk.edu/~yqing/ Yulan Qing] (Tennessee)<br />
|Geometric Boundary of Groups<br />
|Zimmer<br />
|<br />
|-<br />
|February 26<br />
|Blandine Galiay (IHES)<br />
|Divisible convex sets in flag manifolds and rigidity<br />
|Zimmer<br />
|<br />
|-<br />
|March 4<br />
|[http://userhome.brooklyn.cuny.edu/aulicino/ David Aulicino] (Brooklyn College)<br />
|Siegel-Veech Constants of Cyclic Covers of Generic Translation Surfaces<br />
|Apisa<br />
|<br />
|-<br />
|March 11<br />
|[https://aacalderon.com/ Aaron Calderon] (Chicago)<br />
|Equidistribution of twist tori<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|March 18<br />
|[http://sub.mersion.cc Josh Southerland] (Indiana)<br />
|Shrinking targets on square-tiled surfaces<br />
|Fisher<br />
|<br />
|-<br />
|April 1<br />
|[http://www.caglaruyanik.com Caglar Uyanik] (UW)<br />
|Cannon-Thurston maps, random walks, and rigidity<br />
|local<br />
|<br />
|-<br />
|April 8<br />
|[https://math.indiana.edu/about/faculty/bainbridge-matt.html Matt Bainbridge] (Indiana)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|April 15<br />
|[https://math.hunter.cuny.edu/ilyakapo/ Ilya Kapovich] (CUNY)<br />
|TBA<br />
|Uyanik<br />
|<br />
|-<br />
|April 22<br />
|[https://sites.google.com/view/yuchanchang/ Yu-Chan Chang] (Wesleyan)<br />
|TBA<br />
|Dymarz<br />
|<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Kent, Loving, Uyanik<br />
|<br />
|-<br />
|September 23<br />
|[http://www.harrisonbray.com/ Harrison Bray] (George Mason)<br />
|TBA<br />
|Zimmer<br />
|}<br />
<br />
== Spring Abstracts ==<br />
===Aaron Messerla===<br />
<br />
Sela introduced limit groups in his work on the Tarski problem, and showed that each limit group has a cyclic hierarchy. We prove that a class of relatively hyperbolic groups, equipped with a hierarchy similar to the one for limit groups, is closed under quasi-isometry. Additionally, these groups share some of the algebraic properties of limit groups. In this talk I plan to present motivation for and introduce the class of groups studied, as well as present some of the results for this class.<br />
===Mitul Islam===<br />
<br />
The (Hilbert metric) geometry of properly convex domains generalizes real hyperbolic geometry. This generalization is far from the Riemannian notion of non-positive curvature, but they have some intriguing similarities. I will explore this connection from a coarse geometry viewpoint.<br />
The focus will be on Morse geodesics ("negatively curved directions", in a coarse sense) in properly convex domains. I will show that Morse-ness can be characterized entirely using linear algebraic data (i.e. singular values of matrices that track the geodesic). Further, I will discuss how this coarse geometric notion of Morse is related to the symmetric space geometry as well as the smoothness of boundary points. This is joint work with Theodore Weisman.<br />
<br />
===Michael Zshornack===<br />
<br />
Margulis's work on lattices in higher-rank and a number of questions on the existence of surface subgroups motivate the need for understanding arithmetic properties of spaces of surface group representations. In recent work with Jacques Audibert, we outline one possible approach towards understanding such properties for the Hitchin component, one particularly nice space of representations. We utilize the underlying geometry of this space to reduce questions about its arithmetic to questions about the arithmetic of certain algebraic groups, which in turn, allows us to characterize the rational points on these components. In this talk, I'll give an overview of the geometric methods behind the proof of our result and indicate some natural questions about the nature of the resulting surface group actions that follow.<br />
<br />
===Sayantan Khan===<br />
<br />
The moduli spaces of non-orientable hyperbolic surfaces behave significantly differently from their orientable counterparts.<br />
They have infinite volume, almost all geodesic flow orbits escape off to infinity, and the growth of mapping class group orbit points and simple closed curves is believed to have non-integer exponents, unlike in the orientable setting.<br />
In this talk, we outline some of the oddities of these moduli spaces, and outline an approach for studying the dynamics on these spaces via Patterson-Sullivan theory.<br />
A key obstruction to imitating the techniques from the orientable setting is that a number of these techniques rely on the dynamics of the geodesic flow and the mapping class group action on Teichmüller spaces of orientable surfaces, which is not something we can do in the non-orientable setting, since that is what we are trying to prove.<br />
The way around these obstructions is by proving weaker versions of these dynamical statements using a dynamics free approach, which we then use to bootstrap the stronger results.<br />
<br />
===Noelle Sawyer===<br />
<br />
In this talk I will discuss some known results about the geodesics and equilibrium states of the geodesic flow in negative curvature. After, I will introduce some of the tools and techniques needed to show the uniqueness of equilibrium states in the setting of translation surfaces. If time allows, I will talk about some of our upcoming work about the Bernoulli property. This is joint work with Benjamin Call, Dave Constantine, Alena Erchenko, and Grace Work. <br />
===Yulan Qing===<br />
<br />
Gromov boundary provides a useful compactification for all infinite-diameter Gromov hyperbolic spaces. It consists of all geodesic rays starting at a given base-point and it is an essential tool in the study of the coarse geometry of hyperbolic groups. In this talk we generalize the Gromov boundary. We first construct the sublinearly Morse boundaries and show that it is a QI-invariant, metrizable topological space. We show sublinearly Morse directions are generic both in the sense of Patterson-Sullivan and in the sense of random walk. <br />
<br />
The sublinearly Morse boundaries are subsets of all directions with desired properties. In the second half of the talk, we will truly consider the space of all directions and show that with some minimal assumptions on the space, the resulting boundary is a QI-invariant topology space in which many existing boundaries are embedded. This talk is based on a series of work with Kasra Rafi and Giulio Tiozzo.<br />
<br />
===Blandine Galiay===<br />
<br />
Divisible convex sets have been widely studied since the 1960s. They are proper domains of the projective space that admit a cocompact action of a discrete subgroup of the linear projective group. The best-known examples are symmetric spaces embedded in the projective space, but there are also many nonsymmetric examples. It is natural to seek to generalize this theory, by replacing the projective space by a flag variety G/P, where G is a real semisimple non-compact Lie group and P a parabolic of G. A question of van Limbeek and Zimmer is then: are there examples of divisible convex sets in G/P that are nonsymmetric? In a number of cases, it has been proved that there are not. In this talk, we will focus on some particular classes of flag varieties in which rigidity can indeed be observed.<br />
<br />
===David Aulicino===<br />
<br />
We consider generic translation surfaces of genus g>0 with marked points and take covers branched over the marked points such that the monodromy of every element in the fundamental group lies in a cyclic group of order d. Given a translation surface, the number of cylinders with waist curve of length at most L grows like L^2. By work of Veech and Eskin-Masur, when normalizing the number of cylinders by L^2, the limit as L goes to infinity exists and the resulting number is called a Siegel-Veech constant. The same holds true if we weight the cylinders by their area. Remarkably, the Siegel-Veech constant resulting from counting cylinders weighted by area is independent of the number of branch points n. All necessary background will be given and a connection to combinatorics will be presented. This is joint work with Aaron Calderon, Carlos Matheus, Nick Salter, and Martin Schmoll.<br />
<br />
===Aaron Calderon===<br />
Given a hyperbolic surface and a collection of simple closed geodesics, one can build a family of related metrics by cutting open the surface and twisting along the geodesics. This creates to an immersed ``twist torus’’ inside the moduli space of hyperbolic structures, which turns out to be a minimal set for the unipotent-like "earthquake flow." Maryam Mirzakhani famously asked if these twist tori equidistribute when pushed forward under a corresponding geodesic(-like) flow; in this talk, I will explain joint work with James Farre in which we prove that they do equidistribute in some cases, and that they do not in others. The key tool is a bridge that allows for the transfer of ergodic-theoretic results between flat and hyperbolic geometry.<br />
<br />
===Josh Southerland===<br />
<br />
In this talk, we will study a shrinking target problem for square-tiled surfaces. A square-tiled surface is a type of translation surface which arises as a branched cover of the torus (branched over one point). The moduli space of translation surfaces carries an action of $SL^+_2(\R)$, and the stabilizer of this action is called the Veech group. We will show that the action of a subgroup of the Veech group of a square-tiled surface exhibits Diophantine-like properties. This generalizes the work of Finkelshtein, who studied a similar problem on the torus. <br />
<br />
===Caglar Uyanik===<br />
<br />
Cannon and Thurston showed that a hyperbolic 3-manifold that fibers over the circle gives rise to a sphere-filling curve. The universal cover of the fiber surface is quasi-isometric to the hyperbolic plane, whose boundary is a circle, and the universal cover of the 3-manifold is 3-dimensional hyperbolic space, whose boundary is the 2-sphere. Cannon and Thurston showed that the inclusion map between the universal covers extends to a continuous map between their boundaries, whose image is dense. In particular, any measure on the circle pushes forward to a measure on the 2-sphere using this map. We compare several natural measures coming from this construction. This is joint work with Gadre, Haettel, Maher, and Pfaff.<br />
<br />
<br />
===Matt Bainbridge===<br />
===Ilya Kapovich===<br />
===Yu-Chan Chang===<br />
===Chris Leininger===<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
| A metric view of polynomial shift locus<br />
|Wu<br />
|-<br />
|November 20<br />
||[https://sfreedman67.github.io/ Sam Freedman] (Brown)<br />
|Periodic points of Prym eigenforms<br />
|Apisa<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|Non-planarity of SL(2,Z)-orbits of origamis<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|Colloquium by [https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] at 4pm<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
The escaping rates of critical points for polynomials in C[z] induce a continuous and proper map on the moduli space M_d of degree d\ge 2 polynomials. This map has a monotone-light factorization via an intermediate space T_d^* studied by DeMarco and Pilgrim. Restricting on the shift locus S_d of M_d, one obtains the corresponding intermediate space ST_d^*. In this talk, I will relate generic points in S_d to the length functions on the (2d-2)-rose graph and then present an understanding of the natural projectivization of ST_d^* from a metric view. The metric is obtained from thermodynamic metrics on the space of metric graphs. This is a joint work with Yan Mary He.<br />
<br />
===Sam Freedman===<br />
<br />
We will consider the dynamics of affine automorphisms acting on highly symmetric translation surfaces called Veech surfaces. Specifically, we’ll examine the points of the surface that are periodic, i.e., have a finite orbit under the whole automorphism group. While this set is known to be finite for primitive Veech surfaces, for applications it is desirable to determine the periodic points explicitly. In this talk we will discuss our classification of periodic points in the case of minimal Prym eigenforms, certain primitive Veech surfaces in genera 2, 3, and 4.<br />
<br />
===Luke Jeffreys===<br />
<br />
Origamis (also known as square-tiled surfaces) arise naturally in a variety of settings in low-dimensional topology. They can be thought of as generalisations of the torus (the unit square with opposite sides glued) since they are surfaces obtained by gluing the opposite sides of a collection of unit squares. There is a natural action of the matrix group SL(2,Z) on origamis. In genus two (with some extra conditions) the orbits of this action were classified by Hubert-Lelièvre and McMullen. By considering a generating set of size two for SL(2,Z) and varying the number of squares used to build the origamis, we can turn these orbits into an infinite family of four-valent graphs. It is a long-standing conjecture of McMullen that these orbit graphs form a family of expander graphs. In this talk, giving indirect evidence for this conjecture, I will discuss joint work with Carlos Matheus in which we show that these orbit graphs are eventually non-planar - a requirement of any family of expander graphs.<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Sjziemenhttps://wiki.math.wisc.edu/index.php/Whatcha_Doing_SeminarWhatcha Doing Seminar2024-01-08T18:29:21Z<p>Awaldron3: /* Spring 2024 */</p>
<hr />
<div>The Whatcha Doin' Seminar is a place where professors can give 20-30 minute talks about their research aimed at beginning graduate students. This will give students an opportunity to meet potential advisors and see what they are up to.<br />
<br />
Time: '''Mondays''' '''4:00PM-4:30PM'''<br />
<br />
Location: '''Van Vleck B317'''<br />
<br />
== Spring 2024 ==<br />
<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |research area<br />
! align="left" |title<br />
|-<br />
|January 29<br />
|<br />
|<br />
|<br />
|-<br />
|February 5<br />
|<br />
|<br />
|<br />
|-<br />
|February 12<br />
|<br />
|<br />
|<br />
|-<br />
|February 19<br />
|Autumn Kent<br />
|Geometry/Topology/Algebra<br />
|Moduli<br />
|-<br />
|February 26<br />
|Tullia Dymarz <br />
|Geometric Group Theory<br />
|Groups as geometric objects <br />
|-<br />
|March 4<br />
|Andrew Zimmer<br />
|Dynamics/Analysis/Geometry/Topology/Algebra<br />
|Discrete subgroups of Lie groups<br />
|-<br />
|March 11<br />
|Alex Waldron<br />
|Differential geometry<br />
|Geometric flows<br />
|-<br />
|March 18<br />
|Maurice S. Fabien<br />
|Parallel computing/Numerical analysis/Applied Math<br />
|Numerical methods for differential equations<br />
|-<br />
|March 27<br />
|Spring Break<br />
|<br />
|<br />
|-<br />
|April 1<br />
|<br />
|<br />
|<br />
|-<br />
|April 8<br />
|<br />
|<br />
|<br />
|-<br />
|April 15<br />
|Laurel Ohm<br />
|<br />
|PDEs in biofluid dynamics<br />
|-<br />
|April 22<br />
|Dallas Albritton<br />
|Partial Differential Equations<br />
|<br />
|-<br />
|April 29<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
<br />
<br />
<br />
==Spring 2023==<br />
<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |research area<br />
! align="left" |title<br />
|-<br />
|January 30<br />
|Jean-Luc Thiffeault<br />
|Applied Math<br />
|''Active matter''<br />
|-<br />
|February 6<br />
|Dima Arinkin<br />
|Algebraic geometry<br />
|''Formally, differential equations... actually, linear algebra''<br />
|-<br />
|February 13<br />
|Autumn Kent<br />
|Geometry and Topology<br />
|''Moduli'' <br />
|-<br />
|February 20<br />
|Tullia Dymarz<br />
|Geometry, Geometric Group Theory<br />
|Title<br />
|-<br />
|February 27<br />
|No seminar<br />
|<br />
|<br />
|-<br />
|March 6<br />
|Paul Apisa<br />
|Dynamics, geometry, topology<br />
|TBA<br />
|-<br />
|March 13<br />
|Spring Break, No Seminar<br />
|<br />
|<br />
|-<br />
|March 20<br />
|Speaker<br />
|Subject Area<br />
|Title<br />
|-<br />
|March 27<br />
|Sergey Denisov<br />
|Analysis & PDE<br />
|Title<br />
|-<br />
|April 3<br />
|Andrew Zimmer<br />
|TBA<br />
|TBA<br />
|-<br />
|April 10<br />
|No seminar<br />
|<br />
|Title<br />
|-<br />
|April 17<br />
|<br />
|<br />
|Title<br />
|-<br />
||April 24<br />
|Chenxi Wu<br />
|Dynamics<br />
|Title<br />
|-<br />
|May 1<br />
|Marissa Loving<br />
|Geometry, topology, and dynamics<br />
|TBA<br />
|-<br />
|}</div>Sjziemenhttps://wiki.math.wisc.edu/index.php/Spring_2024_Analysis_SeminarSpring 2024 Analysis Seminar2024-01-08T16:43:50Z<p>Sguo223: add a speaker</p>
<hr />
<div>Organizer: Shaoming Guo<br />
<br />
Email: shaomingguo (at) math (dot) wisc (dot) edu<br />
<br />
Time: Wed 3:30--4:30<br />
<br />
Room: B223<br />
<br />
We can use B223 from 4:30 to 5:00 for discussions after talks.<br />
<br />
All talks will be in-person unless otherwise specified.<br />
<br />
In some cases the seminar may be scheduled at different time to accommodate speakers.<br />
<br />
If you would like to subscribe to the Analysis seminar list, send a blank email to analysis+join (at) g-groups (dot) wisc (dot) edu<br />
{| class="wikitable"<br />
|-<br />
|<br />
|Date<br />
|Speaker<br />
|Institution<br />
|Title<br />
|Host<br />
|<br />
|-<br />
|1<br />
|We, Jan. 24, 2024<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|2<br />
|We, Jan. 31<br />
|Sunggeum Hong<br />
|Chosun University<br />
|The Hörmander multiplier theorem for n-linear operators and its applications<br />
|Andreas<br />
|<br />
|-<br />
|3<br />
|We, Feb. 7<br />
|Donald Stull<br />
|University of Chicago<br />
|Dimensions of pinned distance sets in the plane<br />
|Betsy, Shaoming, and Jake F.<br />
|<br />
|-<br />
|4<br />
|We, Feb. 14<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|<br />
|Fr, Feb. 16<br />
|Jack Lutz<br />
|Iowa State University<br />
|Algorithmic Fractal Dimensions<br />
|Shaoming<br />
|department colloquium, 4-5pm<br />
|-<br />
|5<br />
|We, Feb. 21<br />
|''Andrei Martinez-Finkelshtein''<br />
|''Baylor''<br />
|Zeros of polynomials and free probability<br />
|Sergey<br />
|<br />
|-<br />
|6<br />
|We, Feb. 28<br />
|Alex Rutar<br />
|University of St. Andrews<br />
|Dynamical covering arguments via large deviations and non-convex optimization<br />
|Andreas<br />
|<br />
|-<br />
|7<br />
|We, Mar. 6<br />
|Song-Ying Li<br />
|UC-Irvine<br />
|Sup-norm estimates for d-bar and Corona Problems<br />
|Xianghong<br />
|<br />
|-<br />
|8<br />
|We, Mar. 13<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|9<br />
|We, Mar. 20<br />
|Xiaoqi Huang<br />
|LSU<br />
|Curvature and growth rates of log-quasimodes on compact manifolds<br />
|Shaoming<br />
|<br />
|-<br />
|10<br />
|We, Mar. 27<br />
|Spring recess<br />
|spring recess<br />
|<br />
|spring recess<br />
|<br />
|-<br />
|11<br />
|We, Apr. 3<br />
|Shengwen Gan<br />
|UW Madison<br />
|<br />
|<br />
|<br />
|-<br />
|12<br />
|We, Apr. 10<br />
|Victor Bailey<br />
|University of Oklahoma<br />
|<br />
|Betsy<br />
|<br />
|-<br />
|13<br />
|We, Apr. 17<br />
|[https://www.scholars.northwestern.edu/en/persons/jianhui-li Jianhui (Franky) Li]<br />
|Northwestern University<br />
|Weighted Fourier restriction estimate<br />
| Betsy<br />
|<br />
|-<br />
|14<br />
|We, Apr. 24<br />
|Sergey<br />
|UW Madison<br />
|<br />
|<br />
|<br />
|-<br />
|15<br />
|We, May 1<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|}<br />
<br />
==Abstracts==<br />
<br />
<br />
===[[Donald Stull]]===<br />
Title: Dimensions of pinned distance sets in the plane<br />
<br />
Abstract: In this talk, we discuss recent work on the Hausdorff and packing dimension of pinned distance sets in the plane. Given a point x in the plane , and a subset E , the pinned distance set of E with respect to x is the set of all distances between x and the points of E . An important open problem is understanding the Hausdorff, and packing, dimensions of pinned distance sets. We will discuss ongoing progress on this problem, and present improved lower bounds for both the Hausdorff and packing dimensions of pinned distance sets. We also discuss the computability-theoretic methods used to achieve these bounds.<br />
<br />
<br />
===[[Jack Lutz]]===<br />
Title: Algorithmic Fractal Dimensions<br />
<br />
Algorithmic fractal dimensions are computability theoretic versions of Hausdorff dimension and other fractal dimensions. This talk will introduce algorithmic fractal dimensions with particular focus on the Point-to-Set Principle. This principle has enabled several recent proofs of new theorems in geometric measure theory. These theorems, some solving long-standing open problems, are classical (meaning that their statements do not involve computability or logic), even though computability has played a central in their proofs.<br />
<br />
<br />
===[[Andrei Martinez-Finkelshtein]]===<br />
Title: Zeros of polynomials and free probability<br />
<br />
Abstract: I will discuss briefly the connections of some problems from the geometric theory of polynomials to notions from free probability, such as free convolution. More specifically, I will illustrate it with two examples:<br />
- real zeros of some hypergeometric polynomials, their monotonicity, interlacing, and asymptotics;<br />
- flow of zeros of polynomials under iterated differentiation.<br />
<br />
<br />
===[[Alex Rutar]]===<br />
<br />
Title: Dynamical covering arguments via large deviations and non-convex optimization<br />
<br />
Abstract: Most classical notions of fractal dimensions (such as the Hausdorff, box, and Assouad dimensions) are defined in terms of optimal covers, or families of balls minimizing some form of cost function of their radii. For general sets, the optimal covers can be forced to essentially have arbitrary complexity. But for sets satisfying some form of dynamical invariance (which is the case for the majority of well-studied ‘fractal’ sets), one hopes that the underlying dynamics can be used to inform the optimal choice of cover in a meaningful way. In this talk, I will present some techniques drawing on insights from large deviations theory and continuous optimization theory which have proven to be useful technical tools in dimension theory. To highlight these techniques, I will discuss a recent result (joint with Amlan Banaji, Jonathan Fraser, and István Kolossváry) on the dimension theory of sets invariant under certain families of affine transformations in the plane.<br />
<br />
<br />
===[[Song-Ying Li]]===<br />
<br />
Title: Sup-norm estimates for d-bar and Corona problems<br />
<br />
In this talk, we will present some development of Corona problem of several complex variables and discuss its relation to the solution of the sup-norm estimate for d-bar, the Berndtsson conjecture and its application to Corona problem. We will also discuss the application of Hormander weighted L^2 estimates for d-bar to Corona problem.<br />
<br />
===[[Xiaoqi Huang]]===<br />
<br />
Title: Curvature and growth rates of log-quasimodes on compact manifolds<br />
<br />
<br />
Abstract: We will discuss the relation between curvature and L^q norm estimates of spectral projection operators on compact manifolds. We will present a new way that one can hear the shape of compact space forms, if the shape refers to curvature, and the radios used are the L^q-norm of quasimodes. We will also discuss decay rates of L^2-norms over shrinking geodesic tubes for quasimodes under various curvature assumptions. This is based on joint work with Christopher Sogge.<br />
<br />
===Jianhui (Franky) Li===<br />
<br />
Title: Weighted Fourier restriction estimate<br />
<br />
Abstract: We established an $L^p$ weighted Fourier restriction estimate in higher dimensions. In this talk, I will share the intriguing secret behind the crazy exponents found in our induction formula. Surprisingly, these exponents can be computed directly using an intuitive but rough argument. This is a joint work with Xiumin Du, Hong Wang and Ruixiang Zhang.</div>Sjziemenhttps://wiki.math.wisc.edu/index.php/NTS_ABSTRACTSpring2024NTS ABSTRACTSpring20242024-01-08T01:43:28Z<p>Ellenberg: </p>
<hr />
<div><br />
Back to the number theory seminar main webpage: [https://www.math.wisc.edu/wiki/index.php/NTS Main page]<br />
<br />
== Jan 25 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Jason Kountouridis'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The monodromy of simple surface singularities in mixed characteristic<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Given a smooth proper surface X over a $p$-adic field, it is a generally open problem in arithmetic geometry to relate the mod $p$ reduction of X with the monodromy action of inertia on the $\ell$-adic cohomology of X, the latter viewed as a Galois representation ($\ell \neq p$). In this talk, I will focus on the case of X degenerating to a surface with simple singularities, also known as rational double points. This class of singularities is linked to simple simply-laced Lie algebras, and in turn this allows for a concrete description of the associated local monodromy. Along the way we will see how Springer theory enters the picture, and we will discuss a mixed-characteristic version of some classical results of Artin, Brieskorn and Slodowy on simultaneous resolutions.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 01 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Brian Lawrence'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Conditional algorithmic Mordell<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Conditionally on the Fontaine-Mazur, Hodge, and Tate<br />
conjectures, there is an algorithm that finds all rational points on<br />
any curve of genus at least 2 over a number field. The algorithm uses<br />
Faltings's original proof of the finiteness of rational points, along<br />
with an analytic bound on the degree of an isogeny due to Masser and<br />
Wüstholz. (Work in progress with Levent Alpoge.)<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 08 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Haoyang Guo'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Frobenius height of cohomology in mixed characteristic geometry<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In complex geometry, it is known that the i-th cohomology of a variation of Hodge structures on a smooth projective complex variety has the weight increased by at most i. In this talk, we consider the mixed and the positive characteristic analogues of this fact. We recall the notion of prismatic cohomology and prismatic crystals introduced by Bhatt and Scholze, and show that Frobenius height of the i-th prismatic cohomology of a prismatic F-crystal behaves the same. This is a joint work with Shizhang Li.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 15 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Sachi Hashimoto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | p-adic Gross--Zagier and rational points on modular curves<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Faltings' theorem states that there are finitely many rational points on a nice projective curve defined over the rationals of genus at least 2. The quadratic Chabauty method makes explicit some cases of Faltings' theorem. Quadratic Chabauty has recent notable success in determining the rational points of some modular curves. In this talk, I will explain how we can leverage information from p-adic Gross--Zagier formulas to give a new quadratic Chabauty method for certain modular curves. Gross--Zagier formulas relate analytic quantities (special values of p-adic L-functions) to invariants of algebraic cycles (the p-adic height and logarithm of Heegner points). By using p-adic Gross--Zagier formulas, this new quadratic Chabauty method makes essential use of modular forms to determine rational points.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 22 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Zhiyu Zhang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Asai L-functions and twisted arithmetic fundamental lemmas<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Asai L-functions for GLn are related to the arithmetic of Asai motives. The twisted Gan—Gross—Prasad conjecture opens a way of studying (a twist of) central Asai L-values via descents and period integrals. I will consider an arithmetic analog of the conjecture on central derivatives. I will formulate and prove a twisted arithmetic fundamental lemma. The proof is based on new mirabolic special cycles on Rapoport—Zink spaces, and globalization via Kudla—Rapoport cycles and new twisted Hecke cycles on unitary Shimura varieties.<br />
<br />
This talk is given online. Meeting ID: 930 1493 4562 Passcode: 1814<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 29 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Andreas Mihatsch'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Generating series of complex multiplication points<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
A classical result of Zagier states that the degrees of Heegner divisors on the modular curve form the positive Fourier coefficients of a modular form. In my talk, I will define complex multiplication cycles on the Siegel modular variety and show that their degrees have a similar modularity property. This is joint work with Lucas Gerth.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== March 7 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Baying Liu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Recent progress on certain problems related to local Arthur packets of classical groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, I will introduce recent progress on certain problems related to local Arthur packets of classical groups. First, I will introduce a joint work with Freydoon Shahidi towards Jiang's conjecture on the wave front sets of representations in local Arthur packets of classical groups, which is a natural generalization of Shahidi's conjecture, confirming the relation between the structure of wave front sets and the local Arthur parameters. Then, I will introduce a joint work with Alexander Hazeltine and Chi-Heng Lo on the intersection problem of local Arthur packets for symplectic and split odd special orthogonal groups, with applications to the Enhanced Shahidi's conjecture, the closure relation conjecture, and the conjectures of Clozel on unramified representations and automorphic representations. This intersection problem also has been worked out independently at the same time by Hiraku Atobe. In a recent joint work with Alexander Hazeltine, Chi-Heng Lo, and Freydoon Shahidi, we made an upper bound conjecture on wavefront sets of admissible representations of connected reductive groups. If time permits, I will also introduce our recent progress towards this conjecture and its connection with Jiang's conjecture.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 14 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Peter Humphries'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Restricted Arithmetic Quantum Unique Ergodicity<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The quantum unique ergodicity conjecture of Rudnick and Sarnak concerns the mass equidistribution in the large eigenvalue limit of Laplacian eigenfunctions on negatively curved manifolds. This conjecture has been resolved by Lindenstrauss when this manifold is the modular surface assuming these eigenfunctions are additionally Hecke eigenfunctions, namely Hecke-Maass cusp forms. I will discuss a variant of this problem in this arithmetic setting concerning the mass equidistribution of Hecke-Maass cusp forms on submanifolds of the modular surface, along with connections to period integrals of automorphic forms.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 21 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The nontriviality of the Ceresa cycle<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Ceresa cycle is an algebraic 1-cycle in the Jacobian of a smooth algebraic curve with a chosen base point. It is algebraically trivial for a hyperelliptic curve and non-trivial for a very general complex curve of genus at least 3. Given a pointed algebraic curve, there is no general method to determine whether the Ceresa cycle associated to it is rationally or algebraically trivial. In this talk, I will discuss some methods and tools to study this problem.<br />
<br />
|} <br />
</center><br />
<br />
<br></div>Smarshall3https://wiki.math.wisc.edu/index.php/NTS_Fall_Semester_2023NTS Fall Semester 20232024-01-08T01:34:42Z<p>Smarshall3: Created page with "= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison = *'''When:''' Thursdays, 2:30 PM – 3:30 PM, unless otherwise noted *'''Where:''' '''Van Vleck B139''' or remotely *Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link). There is also an accompanying graduate seminar, which meets on Tuesdays.<br> Back to the number theory sem..."</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM, unless otherwise noted<br />
*'''Where:''' '''Van Vleck B139''' or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [[NTSGrad|graduate seminar]], which meets on Tuesdays.<br><br />
<br />
Back to the number theory seminar [https://wiki.math.wisc.edu/index.php/NTS main webpage].<br />
<br />
<br />
<br />
=Fall 2023 Semester=<br />
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<center><br />
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{| 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" |Sept 7<br />
| bgcolor="#F0B0B0" align="center" |Jiaqi Hou (Madison)<br />
| bgcolor="#BCE2FE" | [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2023#Sept_7 Restrictions of eigenfunctions on arithmetic hyperbolic 3-manifolds]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" |Sept 14<br />
| bgcolor="#F0B0B0" align="center" |Ruofan Jiang (Madison)<br />
| bgcolor="#BCE2FE" |[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2023#Sept_14 mod p analogue of Mumford-Tate and André-Oort conjectures for GSpin Shimura varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Sept 21<br />
| bgcolor="#F0B0B0" align="center" |[https://math.uchicago.edu/~iorga/ Andreea Iorga] (U Chicago)<br />
| bgcolor="#BCE2FE" |[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2023#Sept_21 Realising certain semi-direct products as Galois groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Sept 28<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Oct 5<br />
| bgcolor="#F0B0B0" align="center" |[https://sites.google.com/view/zqyang Ziquan Yang] (UW Madison)<br />
| bgcolor="#BCE2FE" |[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2023#Oct_05 Arithmetic Deformation of Line Bundles]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Oct 12<br />
| bgcolor="#F0B0B0" align="center" |Baiqing Zhu (Columbia)<br />
| bgcolor="#BCE2FE" |[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2023#Oct_12 Arithmetic Siegel-Weil formula on the modular curve X_0(N)]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Oct 19<br />
| bgcolor="#F0B0B0" align="center" |Jordan Ellenberg<br />
| bgcolor="#BCE2FE" |What is the mod n Selmer group of a random quadratic twist of an abelian variety over a function field?<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Oct 26<br />
| bgcolor="#F0B0B0" align="center" |Simon Marshall<br />
| bgcolor="#BCE2FE" |[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2023#Oct_26 Large values of eigenfunctions on hyperbolic manifolds]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Nov 2<br />
| bgcolor="#F0B0B0" align="center" |Tonghai Yang<br />
| bgcolor="#BCE2FE" |[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2023#Nov_2 Regularized theta lifting and Complex Multiplication]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Nov 9<br />
| bgcolor="#F0B0B0" align="center" |[https://tungprime.github.io/ Tung Nguyen] (University of Western Ontario)<br />
| bgcolor="#BCE2FE" |[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2023#Nov_9 On the arithmetic of Fekete polynomials of principal Dirichlet characters]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Nov 16<br />
| bgcolor="#F0B0B0" align="center" |Maksym Radziwill (Northwestern)<br />
| bgcolor="#BCE2FE" |[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2023#Nov_16 Gap disribution of <math>\sqrt{n}</math> modulo 1 and the circle method]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Nov 23<br />
| bgcolor="#F0B0B0" align="center" |Thanksgiving - no seminar<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Nov 30<br />
| bgcolor="#F0B0B0" align="center" |Joey Yu Luo<br />
| bgcolor="#BCE2FE" |[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2023#Nov_30 On the arithmetic moduli of unitary Shimura varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Dec 7<br />
| bgcolor="#F0B0B0" align="center" |Chengyang Bao (U Chicago)<br />
| bgcolor="#BCE2FE" |[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2023#Dec_7 Computing crystalline deformation rings via the Taylor--Wiles--Kisin patching method]<br />
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</center><br />
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*to be confirmed<br />
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= Organizer contact information =<br />
<br />
Ziquan Yang zyang352@wisc.edu<br />
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= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
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<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
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<br />
Return to the [[Algebra|Algebra Group Page]]</div>Smarshall3https://wiki.math.wisc.edu/index.php/Applied/ACMS/absF23Applied/ACMS/absF232024-01-03T01:32:27Z<p>Spagnolie: /* ACMS Abstracts: Fall 2023 */</p>
<hr />
<div>= ACMS Abstracts: Fall 2023 =<br />
<br />
=== Erik Bollt (Clarkson University) ===<br />
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Title: A New View on Integrability: On Matching Dynamical Systems through Koopman Operator Eigenfunctions<br />
<br />
Abstract: Matching dynamical systems, through different forms of conjugacies and equivalences, has long been a fundamental concept, and a powerful tool, in the study and classification of non- linear dynamic behavior (e.g. through normal forms). In this presentation we will argue that the use of the Koopman operator and its spectrum are particularly well suited for this endeavor, both in theory, but also especially in view of recent data-driven machine learning algorithmic developments. Recall that the Koopman operator describes the dynamics of observation functions along a flow or map, and it is formally the adjoint of the Frobenius-Perrron operator that describes evolution of densities of ensembles of initial conditions. The Koopman operator has a long theoretical tradition but it has recently become extremely popular through numerical methods such as dynamic mode decomposition (DMD) and variants, for applied problems such as coherence and also in control theory. We demonstrate through illustrative examples that we can nontrivially extend the applicability of the Koopman spectral theoretical and computational machinery beyond modeling and prediction, towards a systematic discovery of rectifying integrability coordinate transformations.<br />
<br />
=== John Schotland (Yale University) ===<br />
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Title: Nonlocal PDEs and Quantum Optics<br />
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Abstract: Quantum optics is the quantum theory of the interaction of light and matter. In this talk, I will describe a real-space formulation of quantum electrodynamics with applications to many body problems. The goal is to understand the transport of nonclassical states of light in random media. In this setting, there is a close relation to kinetic equations for nonlocal PDEs with random coefficients.<br />
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=== Balazs Boros (U Vienna) ===<br />
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Title: Oscillatory mass-action systems<br />
<br />
Abstract: Mass-action differential equations are probably the most common mathematical models in biochemistry, cell biology, and population dynamics. Since oscillatory behavior is ubiquitous in nature, there are several papers (starting with Alfred Lotka) that deal with showing the existence of periodic solutions in mass-action systems. The standard way of proving the existence of a limit cycle in a high-dimensional system is via Andronov-Hopf bifurcation. In this talk, we recall some specific oscillatory models (like glycolysis or phosphorylation), as well as more recent results that aim to systematically classify small mass-action reaction networks that admit an Andronov-Hopf bifurcation.<br />
<br />
=== Peter Jan van Leeuwen (Colorado State University) ===<br />
<br />
Title: Nonlinear Causal Discovery, with applications to atmospheric science<br />
<br />
Abstract: Understanding cause and effect relations in complex systems is one of the main goals of scientific research. Ideally, one sets up controlled experiments in which different potential drivers are varied to infer their influence on a target variable. However, this procedure is impossible in many systems, for example the atmosphere, where nature is doing one experiment for us. An alternative is to build a detailed computer model of the system, and perform controlled experiments in model world. An issue there is that one can only control external drivers, because controlling an internal variable would kill all feedbacks to that variable, resulting in a study of ‘a different planet’. Because many natural systems cannot be controlled, or only partially, we focus on causal discovery in systems that are non-intervenable. I will describe a non-linear causal discovery framework that is based on (conditional) mutual information. It will be shown that conventional analysis of causal relations via so-called Directed Acyclic Graphs (DAGs, se e.g. Pearl and others) is not suitable for nonlinear systems, and an extension is provided that allows for interacting drivers. I prove that the interacting contributions and interaction informations, and provide a solid interpretation of those, in terms of buffering, hampering, and positive feedbacks. Also ways to infer completeness of the causal networks will be discussed, as well as causal relations that are invisible to our framework. The framework will be applied to simple idealized cloud models, and to real very detailed ground-based remote-sensing observations of cloud properties, where we contrast the causal structure of precipitating and non-precipitation strato-cumulus clouds.<br />
<br />
=== Polly Yu (Harvard) ===<br />
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Title: A Spatiotemporal Model of GPCR-G protein Interactions<br />
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Abstract: G-protein coupled receptors (GPCRs) is a class of transmembrane receptors important to many signalling pathways and a common drug target. As its name suggests, the receptor, once activated, binds to a G-protein. Recent experiments suggests that GPCRs form dense tiny clusters. What are the effects of these "hotspots" on signalling kinetics? I will introduce a semi-empirical spatiotemporal model for GPCR-G protein interactions, and present some numerical evidence for how these clusters might locally increase signalling speed. <br />
<br />
=== Da Yang (University of Chicago) ===<br />
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Title: The Incredible Lightness of Water Vapor<br />
<br />
Abstract: Conventional wisdom suggests that warm air rises while cold air sinks. However, recent satellite observations show that, on average, rising air is colder than sinking air in the tropical free troposphere. This is due to the buoyancy effect of water vapor: the molar mass of water vapor is less than that of dry air, making humid air lighter than dry air at the same temperature and pressure. Unfortunately, this vapor buoyancy effect has been considered negligibly small and thereby overlooked in large-scale climate dynamics. Here we use theory, reanalysis data, and a hierarchy of climate models to show that vapor buoyancy has a similar magnitude to thermal buoyancy in the tropical free troposphere. As a result, cold air rises in the tropical free troposphere. We further show that vapor buoyancy enhances thermal radiation, increases subtropical stratiform low clouds, favors convective aggregation, and stabilizes Earth’s climate. However, some state-of-the-art climate models fail to represent vapor buoyancy properly. This flaw leads to inaccurate simulations of cloud distributions—the largest uncertainty in predicting climate change. Implications of our results on paleoclimate and planetary habitability will also be discussed. <br />
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=== Jiaxin Jin (The Ohio State University) ===<br />
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Title: On the Dimension of the R-Disguised Toric Locus of a Reaction Network<br />
<br />
Abstract: The properties of general polynomial dynamical systems can be very difficult to analyze, due to nonlinearity, bifurcations, and the possibility for chaotic dynamics. On the other hand, toric dynamical systems are polynomial dynamical systems that appear naturally as models of reaction networks and have very robust and stable properties. A ''disguised toric dynamical system'' is a polynomial dynamical system generated by a reaction network and some choice of positive parameters, such that it has a toric realization with respect to some other network. Disguised toric dynamical systems enjoy all the robust stability properties of toric dynamical systems. In this project, we study a larger set of dynamical systems where the rate constants are allowed to take both positive and negative values. More precisely, we analyze the R-disguised toric locus of a reaction network, i.e., the subset in the space rate constants (positive or negative) for which the corresponding polynomial dynamical system is disguised toric. In particular, we construct homeomorphisms to provide an exact bound on the dimension of the R-disguised toric locus. <br />
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=== Yuehaw Khoo (Chicago) ===<br />
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Title: Randomized tensor-network algorithms for random data in high-dimensions<br />
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Abstract: Tensor-network ansatz has long been employed to solve the high-dimensional Schrödinger equation, demonstrating linear complexity scaling with respect to dimensionality. Recently, this ansatz has found applications in various machine learning scenarios, including supervised learning and generative modeling, where the data originates from a random process. In this talk, we present a new perspective on randomized linear algebra, showcasing its usage in estimating a density as a tensor-network from i.i.d. samples of a distribution, without the curse of dimensionality, and without the use of optimization techniques. Moreover, we illustrate how this concept can combine the strengths of particle and tensor-network methods for solving high-dimensional PDEs, resulting in enhanced flexibility for both approaches. <br />
<br />
=== Shukai Du (UW) ===<br />
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Title: Element learning: a systematic approach of accelerating finite element-type methods via machine learning, with applications to radiative transfer<br />
<br />
Abstract: In the past decade, (artificial) neural networks and machine learning tools have surfaced as game changing technologies across numerous fields, resolving an array of challenging problems. Even for the numerical solution of partial differential equations (PDEs) or other scientific computing problems, results have shown that machine learning can speed up some computations. However, many machine learning approaches tend to lose some of the advantageous features of traditional numerical PDE methods, such as interpretability and applicability to general domains with complex geometry.<br />
<br />
In this talk, we introduce a systematic approach (which we call element learning) with the goal of accelerating finite element-type methods via machine learning, while also retaining the desirable features of finite element methods. The derivation of this new approach is closely related to hybridizable discontinuous Galerkin (HDG) methods in the sense that the local solvers of HDG are replaced by machine learning approaches. Numerical tests are presented for an example PDE, the radiative transfer equation, in a variety of scenarios with idealized or realistic cloud fields, with smooth or sharp gradient in the cloud boundary transition. Comparisons are set up with either a fixed number of degrees of freedom or a fixed accuracy level of $10^{-3}$ in the relative $L^2$ error, and we observe a significant speed-up with element learning compared to a classical finite element-type method. Reference: [https://arxiv.org/abs/2308.02467 arxiv: 2308.02467]<br />
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=== Lise-Marie Imbert-Gérard (University of Arizona) ===<br />
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Title: Wave propagation in inhomogeneous media with quasi-Trefftz methods<br />
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Abstract: Trefftz methods rely, in broad terms, on the idea of approximating solutions to Partial Differential Equation (PDEs) via Galerkin methods using basis functions which are exact solutions of the PDE, making explicit use of information about the ambient medium. But wave propagation in inhomogeneous media is modeled by PDEs with variable coefficients, and in general no exact solutions are available.<br />
<br />
Quasi-Trefftz methods have been introduced, in the case of the Helmholtz equation with variable coefficients, to address this problem: they rely not on exact solutions to the PDE but instead of high order approximate solutions constructed locally. We will discuss the origin, the construction, and the properties of these so-called quasi-Trefftz functions. We will also discuss the consistency error introduced by this construction process.<br />
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=== Timothy Atherton (Tufts University) ===<br />
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Title: Shape optimization and shapeshifting in soft matter<br />
<br />
Abstract: Soft materials are ubiquitous in everyday life and are ideal candidates for advanced engineering applications including soft, biomimetic robots, self-building machines, shape-shifters, artificial muscles, and chemical delivery packages. In many of these, the material must make a dramatic change in shape with an accompanying re-ordering of the material; in others changes in the ordering can be used to drive or even interrupt shape change. To optimize the materials and structures, it is necessary to have a detailed understanding of how the microstructure and macroscopic shape co-evolve. In this talk, I will therefore discuss the interactions between order and shape evolution with examples primarily drawn from my group's work on emulsions, liquid crystals and other soft materials. All of these efforts draw upon mathematics, including finite elements, optimization theory and beyond.<br />
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=== Daphne Klotsa (UNC Chapel Hill) ===<br />
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Title: A touch of non-linearity: mesoscale swimmers and active matter in fluids<br />
<br />
Abstract: Living matter, such as biological tissue, can be seen as a nonequilibrium hierarchical assembly of assemblies of smaller and smaller active components, where energy is consumed at many scales. The remarkable properties of such living or “active-matter” systems make them promising candidates to study and synthetically design. While many active-matter systems reside in fluids (solution, blood, ocean, air), so far, studies that include hydrodynamic interactions have focussed on microscopic scales in Stokes flows. At those microscopic scales viscosity dominates, and inertia can be neglected. What happens as swimmers slightly increase in size (say ~0.1mm-100cm) or as they form larger aggregates and swarms? The system then enters the intermediate Reynolds regime where both inertia and viscosity play a role, and where nonlinearities are introduced in the fluid. In this talk, I will present a simple model swimmer used to understand the transition from Stokes to intermediate Reynolds numbers, first for a single swimmer, then for pairwise interactions and finally for collective behavior. We show that, even for a simple model, inertia can induce hydrodynamic interactions that generate novel phase behavior, steady states and transitions.<br />
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=== Adam Stinchcombe (U Toronto) ===<br />
<br />
Title: A simulation of the electrical activity of retinal tissue and electroretinogram design<br />
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Abstract: An electroretinogram (ERG) is a diagnostic test that measures the electrical activity of the neuronal cells of the retina. A light stimulus causes transmembrane currents in the photoreceptors (the rods and cones) and in the other retinal neurons via synaptic connections with the photoreceptors. These currents are detected by electrodes on the surface of the eye. We use an extended bidomain framework to model the whole-tissue electrical activity of the retina. Detailed ionic current models of the rods, cones, and bipolar cells, including the phototransduction pathway and the neuronal connectivity of the retina, are coupled to an elliptic PDE for the electrostatic potential inside the interior of the eye. To numerically integrate the stiff dynamics, we employ an adaptive time-stepping routine, a Newton iteration, and an efficient spatial discretization of the PDE. The simulation provides a physical basis for the a-waves in ERG recordings used by ophthalmologists to diagnose disease. For ERG recordings indicative of disease, we solve an inverse problem to infer a biophysical basis of the retinal disease. We solve a numerical optimal control problem to design a light stimulus to produce an efficient, patient-specific, and adaptive diagnosis procedure.</div>Spagnoliehttps://wiki.math.wisc.edu/index.php/Past_Probability_Seminars_Fall_2023Past Probability Seminars Fall 20232024-01-02T16:45:23Z<p>Valko: Created page with "Past Seminars = Fall 2023 = <b>Thursdays at 2:30 PM either in 901 Van Vleck Hall or on Zoom</b> We usually end for questions at 3:20 PM. == September 14, 2023: [https://www.mathjunge.com/ Matthew Junge] (CUNY) == '''The frog model on trees''' The frog model describes random activation and spread. Think combustion or an epidemic. I have studied these dynamics on ''d''-ary trees for ten years. I will discuss our progress and what remains to be done. == September 2..."</p>
<hr />
<div>[[Past Seminars]]<br />
<br />
= Fall 2023 =<br />
<b>Thursdays at 2:30 PM either in 901 Van Vleck Hall or on Zoom</b><br />
<br />
We usually end for questions at 3:20 PM.<br />
<br />
== September 14, 2023: [https://www.mathjunge.com/ Matthew Junge] (CUNY) ==<br />
'''The frog model on trees'''<br />
<br />
The frog model describes random activation and spread. Think combustion or an epidemic. I have studied these dynamics on ''d''-ary trees for ten years. I will discuss our progress and what remains to be done.<br />
<br />
== September 21, 2023: [https://yierlin.me/ Yier Lin] (U. Chicago) ==<br />
'''Large Deviations of the KPZ Equation and Most Probable Shapes'''<br />
<br />
<br />
The KPZ equation is a stochastic PDE that plays a central role in a class of random growth phenomena. In this talk, we will explore the Freidlin-Wentzell LDP for the KPZ equation through the lens of the variational principle. Additionally, we will explain how to extract various limits of the most probable shape of the KPZ equation using the variational formula. We will also discuss an alternative approach for studying these quantities using the method of moments. This talk is based in part on joint works with Pierre Yves Gaudreau Lamarre and Li-Cheng Tsai.<br />
<br />
== September 28, 2023: [https://warwick.ac.uk/fac/sci/statistics/staff/academic-research/rosati/ Tommaso Rosati] (U. Warwick) ==<br />
'''The Allen-Cahn equation with weakly critical initial datum'''<br />
<br />
We study the 2D Allen-Cahn with white noise initial datum. In a weak coupling regime, where the nonlinearity is damped in relation to the smoothing of the initial condition, we prove Gaussian fluctuations. The effective variance that appears can be described as the solution to an ODE. Our proof builds on a Wild expansion of the solution, which is controlled through precise combinatorial estimates. Joint work with Simon Gabriel and Nikolaos Zygouras.<br />
<br />
== October 5, 2023: ==<br />
'''Abstract, title: TBA'''<br />
<br />
== October 12, 2023: No Seminar ([https://sites.math.northwestern.edu/mwp/ Midwest Probability Colloquium]) ==<br />
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== October 19, 2023: [https://www.paulduncan.net/ Paul Duncan] (Hebrew University of Jerusalem) ==<br />
'''Deconfinement in Ising Lattice Gauge Theory'''<br />
<br />
A lattice gauge theory is a random assignment of spins to edges of a lattice that offers a more tractable model in which to study path integrals that appear in particle physics. We demonstrate the existence of a phase transition corresponding to deconfinement in a simplified model called Ising lattice gauge theory on the cubical lattice Z^3. Our methods involve studying the topology of a random 2-dimensional cubical complex on Z^3 called random-cluster plaquette percolation, which in turn can be reduced to the study of a random dual graph. No prior background in topology or physics will be assumed. This is based on joint work with Benjamin Schweinhart.<br />
<br />
== October 26, 2023: Yuchen Liao (UW - Madison) ==<br />
'''Large deviations for the deformed Polynuclear growth'''<br />
<br />
The polynuclear growth model (PNG) is a prototypical example of random interface growth among the Kardar-Parisi-Zhang universality class. In this talk I will discuss a q-deformation of the PNG model recently introduced by Aggarwal-Borodin-Wheeler. We are mainly interested in the large time large deviations of the one-point distribution under narrow-wedge (droplet) initial data, i.e., the rare events that the height function at time t being much larger (upper tail) or much smaller (lower tail) than its expected value. Large deviation principles with speed t and t^2 are established for the upper and lower tails, respectively. The upper tail rate function is computed explicitly and is independent of q. The lower tail rate function is described through a variational problem and shows nontrivial q-dependence. Based on joint work with Matteo Mucciconi and Sayan Das.<br />
<br />
== November 2, 2023: [http://homepages.math.uic.edu/~couyang/ Cheng Ouyang] (U. Illinois Chicago) ==<br />
'''Colored noise and parabolic Anderson model on Torus'''<br />
<br />
We construct an intrinsic family of Gaussian noises on compact Riemannian manifolds which we call the colored noise on manifolds. It consists of noises with a wide range of singularities. Using this family of noises, we study the parabolic Anderson model on compact manifolds. To begin with, we started our investigation on a flat torus and established existence and uniqueness of the solution, as well as some sharp bounds on the second moment of the solution. In particular, our methodology does not necessarily rely on Fourier analysis and can be applied to study the PAM on more general manifolds.<br />
<br />
== November 9, 2023: [https://scottandrewsmith.github.io/ Scott Smith] (Chinese Academy of Sciences) ==<br />
'''A stochastic analysis viewpoint on the master loop equation for lattice Yang-Mills''' <br />
<br />
I will discuss the master loop equation for lattice Yang-Mills, introduced in the physics literature by Makeenko/Migdal (1979). A more precise formulation and proof was given by Chatterjee (2019) for SO(N) and later by Jafarov for SU(N). I will explain how the loop equation arises naturally from the Langevin dynamic for the lattice Yang-Mills measure. Based on joint work with Hao Shen and Rongchan Zhu.<br />
<br />
== November 16, 2023: [https://math.mit.edu/~mnicolet/ Matthew Nicoletti] (MIT) ==<br />
'''Colored Interacting Particle Systems on the Ring: Stationary Measures from Yang--Baxter Equation'''<br />
<br />
Recently, there has been much progress in understanding stationary measures for colored (also called multi-species or multi-type) interacting particle systems, motivated by asymptotic phenomena and rich underlying algebraic and combinatorial structures (such as nonsymmetric Macdonald polynomials).<br />
<br />
In this work, we present a unified approach to constructing stationary measures for several colored particle systems on the ring and the line, including (1)~the Asymmetric Simple Exclusion Process (mASEP); (2)~the $q$-deformed Totally Asymmetric Zero Range Process (TAZRP) also known as the $q$-Boson particle system; (3)~the $q$-deformed Pushing Totally Asymmetric Simple Exclusion Process ($q$-PushTASEP). Our method is based on integrable stochastic vertex models and the Yang--Baxter equation. We express the stationary measures as partition functions of new ``queue vertex models<nowiki>''</nowiki> on the cylinder. The stationarity property is a direct consequence of the Yang--Baxter equation. This is joint work with A. Aggarwal and L. Petrov.<br />
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== November 23, 2023: No Seminar ==<br />
'''No seminar. Thanksgiving.'''<br />
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== November 30, 2023: [http://web.mit.edu/youngtak/www/homepage.html Youngtak Sohn] (MIT) ==<br />
'''Geometry of random constraint satisfaction problems'''<br />
<br />
The framework of constraint satisfaction problem (CSP) captures many fundamental problems in combinatorics and computer science, such as finding a proper coloring of a graph or solving the boolean satisfiability problems. Solving a CSP can often be NP-hard in the worst-case scenario. To study the typical cases of CSPs, statistical physicists have proposed a detailed picture of the solution space for random CSPs based on non-rigorous methods from spin glass theory. In this talk, I will first survey the conjectured rich phase diagrams of random CSPs in the one-step replica symmetry breaking (1RSB) universality class. Then, I will describe the recent progress in understanding the global and local geometry of solutions, particularly in random regular NAE-SAT problem. <br />
<br />
This talk is based on joint works with Danny Nam and Allan Sly.<br />
<br />
== December 7, 2023: Minjae Park (U. Chicago) ==<br />
'''Yang-Mills theory and random surfaces'''<br />
<br />
I will talk about some recent work on Yang-Mills theory for classical Lie groups and its relationship to the theory of random surfaces. In particular, I will explain how Wilson loop expectations in lattice Yang-Mills can be expressed as sums over embedded planar maps for any matrix dimension N ≥ 1, any inverse temperature β > 0, and any lattice dimension d ≥ 2. The main idea is from my similar result for 2D continuum Yang-Mills (with Joshua Pfeffer, Scott Sheffield, and Pu Yu), and it gives alternative derivations and interpretations of several recent theorems including Brownian motion limits (Dahlqvist), lattice string trajectories (Chatterjee and Jafarov), and surface sums (Magee and Puder). Based on joint work with Sky Cao and Scott Sheffield.</div>Valkohttps://wiki.math.wisc.edu/index.php/Past_Probability_Seminars_Fall_2024Past Probability Seminars Fall 20242024-01-02T16:44:17Z<p>Valko: Replaced content with "Past Seminars = Fall 2024 = <b>Thursdays at 2:30 PM either in 901 Van Vleck Hall or on Zoom</b> We usually end for questions at 3:20 PM."</p>
<hr />
<div>[[Past Seminars]]<br />
<br />
= Fall 2024 =<br />
<b>Thursdays at 2:30 PM either in 901 Van Vleck Hall or on Zoom</b><br />
<br />
We usually end for questions at 3:20 PM.</div>Valkohttps://wiki.math.wisc.edu/index.php/NTSGrad_Spring_2024NTSGrad Spring 20242023-12-31T06:18:18Z<p>Tbhatnagar2: </p>
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<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:25 PM – 3:25 PM<br />
*'''Where:''' Van Vleck Hall, B139<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| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and sometimes try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Spring2024 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="#D0D0D0" width="300" align="center" |1/23<br />
| bgcolor="#F0A0A0" width="300" align="center" |[https://sites.google.com/view/tbhatnagar/home?authuser=0 Tejasi Bhatnagar]<br />
| bgcolor="#BCD2EE" width="300" align="center" |[[NTSGrad_Spring_2024/Abstracts#1/23|Stratification in the moduli space of abelian varieties in char p.]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |1/30<br />
| bgcolor="#F0A0A0" width="300" align="center" |Joey Yu Luo<br />
| bgcolor="#BCD2EE" width="300" align="center" |[[NTSGrad_Spring_2024/Abstracts#1/30|Gross-Zagier formula: a motivation.]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |2/6<br />
| bgcolor="#F0A0A0" width="300" align="center" |Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center" |[[NTSGrad Spring 2024/Abstracts#2/6|A Zoo of L-functions]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |2/13<br />
| bgcolor="#F0A0A0" width="300" align="center" |Sun Woo Park<br />
| bgcolor="#BCD2EE" width="300" align="center" |[[NTSGrad Spring 2024/Abstracts#2/13|Counting integer solutions of $x^2+y^2=r$ satisfying prime divisibility conditions]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |2/20<br />
| bgcolor="#F0A0A0" width="300" align="center" |Eiki Norizuki<br />
| bgcolor="#BCD2EE" width="300" align="center" |[[NTSGrad_Spring_2024/Abstracts#2/20|Abelian Varieties over C]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |2/27<br />
| bgcolor="#F0A0A0" width="300" align="center" |No Speaker<br />
| bgcolor="#BCD2EE" width="300" align="center" |<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |3/5<br />
| bgcolor="#F0A0A0" width="300" align="center" |No Talk!<br />
| bgcolor="#BCD2EE" width="300" align="center" |Arizona Winter School<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |3/12<br />
| bgcolor="#F0A0A0" width="300" align="center" |Sun Woo Park<br />
| bgcolor="#BCD2EE" width="300" align="center" |Counting integer solutions of $x^2+y^2=r$ satisfying prime divisibility conditions (Part 2)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |3/19<br />
| bgcolor="#F0A0A0" width="300" align="center" |Yifan Wei<br />
| bgcolor="#BCD2EE" width="300" align="center" |[[NTSGrad_Spring_2024/Abstracts#3/19|Periods and Class Field Theory]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |3/26<br />
| bgcolor="#F0A0A0" width="300" align="center" |No Talk!<br />
| bgcolor="#BCD2EE" width="300" align="center" |Spring Break<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |4/2<br />
| bgcolor="#F0A0A0" width="300" align="center" |<br />
| bgcolor="#BCD2EE" width="300" align="center" |<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |4/9<br />
| bgcolor="#F0A0A0" width="300" align="center" |<br />
| bgcolor="#BCD2EE" width="300" align="center" |<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |4/16<br />
| bgcolor="#F0A0A0" width="300" align="center" |Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center" |Thesis Defence! (Room TBD)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |4/23<br />
| bgcolor="#F0A0A0" width="300" align="center" |John Yin<br />
| bgcolor="#BCD2EE" width="300" align="center" |Thesis Defence! (Room TBD)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |4/30<br />
| bgcolor="#F0A0A0" width="300" align="center" |<br />
| bgcolor="#BCD2EE" width="300" align="center" |<br />
|-<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
=Organizer(s)=<br />
<br />
[https://sites.google.com/view/tbhatnagar/about-me Tejasi Bhatnagar] (tbhatnagar2@wisc.edu)<br />
<br />
[https://sites.google.com/view/jiaqihou/home Jiaqi Hou] (jhou39@wisc.edu)<br />
<br />
==Former Organizers==<br />
<br />
Hyun Jong Kim<br />
<br />
John Yin<br />
<br />
Jerry Yu Fu <br />
<br />
Brandon Boggess<br />
<br />
Soumya Sankar<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 2023 is [[NTSGrad_Fall_2023|here]].<br><br />
The seminar webpage for Spring 2023 is [[NTSGrad_Spring_2023|here]].<br><br />
The seminar webpage for Fall 2022 is [[NTSGrad_Fall_2022|here]].<br><br />
The seminar webpage for Spring 2022 is [[NTSGrad_Spring_2022|here]].<br><br />
The seminar webpage for Fall 2021 is [[NTSGrad_Fall_2021|here]].<br><br />
The seminar webpage for Spring 2021 is [[NTSGrad_Spring_2021|here]].<br><br />
The seminar webpage for Fall 2020 is [[NTSGrad_Fall_2020|here]].<br><br />
The seminar webpage for Spring 2020 is [[NTSGrad_Spring_2020|here]].<br><br />
The seminar webpage for Fall 2019 is [[NTSGrad_Fall_2019|here]].<br><br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<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 [[NTSGrad|GNTS Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Jhou39