https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Bolotin&feedformat=atomUW-Math Wiki - User contributions [en]2021-01-28T12:59:27ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18593Colloquia/Spring20202020-01-04T07:34:53Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm Room 911'''<br />
|Andrew Zimmer (LSU)<br />
|[[#Andrew Zimmer (LSU)| "Intrinsic and extrinsic geometries in several complex variables"]]<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Charlotte Chan (MIT)<br />
|[[#Charlotte Chan (MIT)|"Flag varieties and representations of p-adic groups"]]<br />
|Erman<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday 2:30-3:30pm Room 911'''<br />
|Alex Waldron (Michigan)<br />
|[[#Alex Waldron (Michigan)|Gauge theory and geometric flows]]<br />
|Paul<br />
|-<br />
|Dec 11 '''Wednesday 4-5pm'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|-<br />
|Dec 13 <br />
|Chenxi Wu (Rutgers)<br />
|[[#Chenxi Wu (Rutgers)|Kazhdan's theorem on metric graphs]]<br />
|Ellenberg<br />
|-<br />
|Dec 18 '''Wednesday 4-5pm'''<br />
|Ruobing Zhang (Stony Brook)<br />
|[[#Ruobing Zhang (Stony Brook)|Geometry and analysis of degenerating Calabi-Yau manifolds]]<br />
|Paul<br />
|-<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 10<br />
|Thomas Lam (Michigan) <br />
|[[#Thomas Lam (Michigan) |Positive geometries and string theory amplitudes]]<br />
|Erman<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|<br />
|Soskova/Lempp<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 23<br />
|Martin Hairer (Imperial College London)<br />
|Wolfgang Wasow Lecture<br />
|Hao Shen<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chan (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
=== Alex Waldron (Michigan) ===<br />
<br />
Title: Gauge theory and geometric flows<br />
<br />
Abstract: I will give a brief introduction to two major areas of research in differential geometry: gauge theory and geometric flows. I'll then introduce a geometric flow (Yang-Mills flow) arising from a variational problem with origins in physics, which has been studied by geometric analysts since the early 1980s. I'll conclude by discussing my own work on the behavior of Yang-Mills flow in the critical dimension (n = 4).<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
=== Chenxi Wu (Rutgers) ===<br />
<br />
Title: Kazhdan's theorem on metric graphs<br />
<br />
Abstract: I will give an introduction to the concept of canonical (arakelov) metric on a metric graph, which is related to combinatorial questions like the counting of spanning trees, and generalizes the corresponding concept on Riemann surfaces. I will also present a recent result in collaboration with Farbod Shokrieh on the convergence of canonical metric under normal covers.<br />
<br />
=== Ruobing Zhang (Stony Brook) ===<br />
<br />
Title: Geometry and analysis of degenerating Calabi-Yau manifolds<br />
<br />
Abstract: This talk concerns a naturally occurring family of degenerating Calabi-Yau manifolds. A primary tool in analyzing their behavior is to combine the recently developed structure theory for Einstein manifolds and multi-scale singularity analysis for degenerating nonlinear PDEs in the collapsed setting. Based on the algebraic degeneration, we will give precise and more quantitative descriptions of singularity formation from both metric and analytic points of view.<br />
<br />
=== Thomas Lam (Michigan) === <br />
<br />
Title: Positive geometries and string theory amplitudes<br />
<br />
Abstract: Inspired by developments in quantum field theory, we<br />
recently defined the notion of a positive geometry, a class of spaces<br />
that includes convex polytopes, positive parts of projective toric<br />
varieties, and positive parts of flag varieties. I will discuss some<br />
basic features of the theory and an application to genus zero string<br />
theory amplitudes. As a special case, we obtain the Euler beta<br />
function, familiar to mathematicians, as the "stringy canonical form"<br />
of the closed interval.<br />
<br />
This talk is based on joint work with Arkani-Hamed, Bai, and He.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18560Colloquia/Spring20202019-12-18T19:08:15Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm Room 911'''<br />
|Andrew Zimmer (LSU)<br />
|[[#Andrew Zimmer (LSU)| "Intrinsic and extrinsic geometries in several complex variables"]]<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Charlotte Chan (MIT)<br />
|[[#Charlotte Chan (MIT)|"Flag varieties and representations of p-adic groups"]]<br />
|Erman<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday 2:30-3:30pm Room 911'''<br />
|Alex Waldron (Michigan)<br />
|[[#Alex Waldron (Michigan)|Gauge theory and geometric flows]]<br />
|Paul<br />
|-<br />
|Dec 11 '''Wednesday 4-5pm'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|-<br />
|Dec 13 <br />
|Chenxi Wu (Rutgers)<br />
|[[#Chenxi Wu (Rutgers)|Kazhdan's theorem on metric graphs]]<br />
|Ellenberg<br />
|-<br />
|Dec 18 '''Wednesday 4-5pm'''<br />
|Ruobing Zhang (Stony Brook)<br />
|[[#Ruobing Zhang (Stony Brook)|Geometry and analysis of degenerating Calabi-Yau manifolds]]<br />
|Paul<br />
|-<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 10<br />
|Thomas Lam (Michigan) <br />
|<br />
|Erman<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|<br />
|Soskova/Lempp<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chan (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
=== Alex Waldron (Michigan) ===<br />
<br />
Title: Gauge theory and geometric flows<br />
<br />
Abstract: I will give a brief introduction to two major areas of research in differential geometry: gauge theory and geometric flows. I'll then introduce a geometric flow (Yang-Mills flow) arising from a variational problem with origins in physics, which has been studied by geometric analysts since the early 1980s. I'll conclude by discussing my own work on the behavior of Yang-Mills flow in the critical dimension (n = 4).<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
=== Chenxi Wu (Rutgers) ===<br />
<br />
Title: Kazhdan's theorem on metric graphs<br />
<br />
Abstract: I will give an introduction to the concept of canonical (arakelov) metric on a metric graph, which is related to combinatorial questions like the counting of spanning trees, and generalizes the corresponding concept on Riemann surfaces. I will also present a recent result in collaboration with Farbod Shokrieh on the convergence of canonical metric under normal covers.<br />
<br />
=== Ruobing Zhang (Stony Brook) ===<br />
<br />
Title: Geometry and analysis of degenerating Calabi-Yau manifolds<br />
<br />
Abstract: This talk concerns a naturally occurring family of degenerating Calabi-Yau manifolds. A primary tool in analyzing their behavior is to combine the recently developed structure theory for Einstein manifolds and multi-scale singularity analysis for degenerating nonlinear PDEs in the collapsed setting. Based on the algebraic degeneration, we will give precise and more quantitative descriptions of singularity formation from both metric and analytic points of view.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18546Colloquia/Spring20202019-12-10T05:20:49Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm Room 911'''<br />
|Andrew Zimmer (LSU)<br />
|[[#Andrew Zimmer (LSU)| "Intrinsic and extrinsic geometries in several complex variables"]]<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Charlotte Chan (MIT)<br />
|[[#Charlotte Chan (MIT)|"Flag varieties and representations of p-adic groups"]]<br />
|Erman<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday 2:30-3:30pm Room 911'''<br />
|Alex Waldron (Michigan)<br />
|[[#Alex Waldron (Michigan)|Gauge theory and geometric flows]]<br />
|Paul<br />
|-<br />
|Dec 11 '''Wednesday 4-5pm'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|-<br />
|Dec 13 <br />
|Chenxi Wu (Rutgers)<br />
|[[#Chenxi Wu (Rutgers)|Kazhdan's theorem on metric graphs]]<br />
|Ellenberg<br />
|-<br />
|Dec 18 '''Wednesday 4-5pm'''<br />
|Ruobing Zhang (Stony Brook)<br />
|[[#Ruobing Zhang (Stony Brook)|Geometry and analysis of degenerating Calabi-Yau manifolds]]<br />
|Paul<br />
|-<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|<br />
|Soskova/Lempp<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chan (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
=== Alex Waldron (Michigan) ===<br />
<br />
Title: Gauge theory and geometric flows<br />
<br />
Abstract: I will give a brief introduction to two major areas of research in differential geometry: gauge theory and geometric flows. I'll then introduce a geometric flow (Yang-Mills flow) arising from a variational problem with origins in physics, which has been studied by geometric analysts since the early 1980s. I'll conclude by discussing my own work on the behavior of Yang-Mills flow in the critical dimension (n = 4).<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
=== Chenxi Wu (Rutgers) ===<br />
<br />
Title: Kazhdan's theorem on metric graphs<br />
<br />
Abstract: I will give an introduction to the concept of canonical (arakelov) metric on a metric graph, which is related to combinatorial questions like the counting of spanning trees, and generalizes the corresponding concept on Riemann surfaces. I will also present a recent result in collaboration with Farbod Shokrieh on the convergence of canonical metric under normal covers.<br />
<br />
=== Ruobing Zhang (Stony Brook) ===<br />
<br />
Title: Geometry and analysis of degenerating Calabi-Yau manifolds<br />
<br />
Abstract: This talk concerns a naturally occurring family of degenerating Calabi-Yau manifolds. A primary tool in analyzing their behavior is to combine the recently developed structure theory for Einstein manifolds and multi-scale singularity analysis for degenerating nonlinear PDEs in the collapsed setting. Based on the algebraic degeneration, we will give precise and more quantitative descriptions of singularity formation from both metric and analytic points of view.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18545Colloquia/Spring20202019-12-10T05:18:02Z<p>Bolotin: /* Fall 2019 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm Room 911'''<br />
|Andrew Zimmer (LSU)<br />
|[[#Andrew Zimmer (LSU)| "Intrinsic and extrinsic geometries in several complex variables"]]<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Charlotte Chan (MIT)<br />
|[[#Charlotte Chan (MIT)|"Flag varieties and representations of p-adic groups"]]<br />
|Erman<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday 2:30-3:30pm Room 911'''<br />
|Alex Waldron (Michigan)<br />
|[[#Alex Waldron (Michigan)|Gauge theory and geometric flows]]<br />
|Paul<br />
|-<br />
|Dec 11 '''Wednesday 4-5pm'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|-<br />
|Dec 13 <br />
|Chenxi Wu (Rutgers)<br />
|[[#Chenxi Wu (Rutgers)|Kazhdan's theorem on metric graphs]]<br />
|Ellenberg<br />
|-<br />
|Dec 18 '''Wednesday 4-5pm'''<br />
|Ruobing Zhang (Stony Brook)<br />
|[[#Ruobing Zhang (Stony Brook)|Geometry and analysis of degenerating Calabi-Yau manifolds]]<br />
|Paul<br />
|-<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|<br />
|Soskova/Lempp<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chan (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
=== Alex Waldron (Michigan) ===<br />
<br />
Title: Gauge theory and geometric flows<br />
<br />
Abstract: I will give a brief introduction to two major areas of research in differential geometry: gauge theory and geometric flows. I'll then introduce a geometric flow (Yang-Mills flow) arising from a variational problem with origins in physics, which has been studied by geometric analysts since the early 1980s. I'll conclude by discussing my own work on the behavior of Yang-Mills flow in the critical dimension (n = 4).<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
=== Ruobing Zhang (Stony Brook) ===<br />
<br />
Title: Geometry and analysis of degenerating Calabi-Yau manifolds<br />
<br />
Abstract: This talk concerns a naturally occurring family of degenerating Calabi-Yau manifolds. A primary tool in analyzing their behavior is to combine the recently developed structure theory for Einstein manifolds and multi-scale singularity analysis for degenerating nonlinear PDEs in the collapsed setting. Based on the algebraic degeneration, we will give precise and more quantitative descriptions of singularity formation from both metric and analytic points of view.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18535Colloquia/Spring20202019-12-09T05:07:36Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm Room 911'''<br />
|Andrew Zimmer (LSU)<br />
|[[#Andrew Zimmer (LSU)| "Intrinsic and extrinsic geometries in several complex variables"]]<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Charlotte Chan (MIT)<br />
|[[#Charlotte Chan (MIT)|"Flag varieties and representations of p-adic groups"]]<br />
|Erman<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday 2:30-3:30pm Room 911'''<br />
|Alex Waldron (Michigan)<br />
|[[#Alex Waldron (Michigan)|Gauge theory and geometric flows]]<br />
|Paul<br />
|-<br />
|Dec 11 '''Wednesday 4-5pm'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|-<br />
|Dec 13 <br />
|Chenxi Wu (Rutgers)<br />
|<br />
|Erman<br />
|-<br />
|Dec 18 '''Wednesday 4-5pm'''<br />
|Ruobing Zhang (Stony Brook)<br />
|[[#Ruobing Zhang (Stony Brook)|Geometry and analysis of degenerating Calabi-Yau manifolds]]<br />
|Paul<br />
|-<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|<br />
|Soskova/Lempp<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chan (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
=== Alex Waldron (Michigan) ===<br />
<br />
Title: Gauge theory and geometric flows<br />
<br />
Abstract: I will give a brief introduction to two major areas of research in differential geometry: gauge theory and geometric flows. I'll then introduce a geometric flow (Yang-Mills flow) arising from a variational problem with origins in physics, which has been studied by geometric analysts since the early 1980s. I'll conclude by discussing my own work on the behavior of Yang-Mills flow in the critical dimension (n = 4).<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
=== Ruobing Zhang (Stony Brook) ===<br />
<br />
Title: Geometry and analysis of degenerating Calabi-Yau manifolds<br />
<br />
Abstract: This talk concerns a naturally occurring family of degenerating Calabi-Yau manifolds. A primary tool in analyzing their behavior is to combine the recently developed structure theory for Einstein manifolds and multi-scale singularity analysis for degenerating nonlinear PDEs in the collapsed setting. Based on the algebraic degeneration, we will give precise and more quantitative descriptions of singularity formation from both metric and analytic points of view.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18532Colloquia/Spring20202019-12-06T22:19:20Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm Room 911'''<br />
|Andrew Zimmer (LSU)<br />
|[[#Andrew Zimmer (LSU)| "Intrinsic and extrinsic geometries in several complex variables"]]<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Charlotte Chan (MIT)<br />
|[[#Charlotte Chan (MIT)|"Flag varieties and representations of p-adic groups"]]<br />
|Erman<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday 2:30-3:30pm Room 911'''<br />
|Alex Waldron (Michigan)<br />
|[[#Alex Waldron (Michigan)|Gauge theory and geometric flows]]<br />
|Paul<br />
|-<br />
|Dec 11 '''Wednesday 4-5pm'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|-<br />
|Dec 13 <br />
|Chenxi Wu (Rutgers)<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|<br />
|Soskova/Lempp<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chan (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
=== Alex Waldron (Michigan) ===<br />
<br />
Title: Gauge theory and geometric flows<br />
<br />
Abstract: I will give a brief introduction to two major areas of research in differential geometry: gauge theory and geometric flows. I'll then introduce a geometric flow (Yang-Mills flow) arising from a variational problem with origins in physics, which has been studied by geometric analysts since the early 1980s. I'll conclude by discussing my own work on the behavior of Yang-Mills flow in the critical dimension (n = 4).<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18517Colloquia/Spring20202019-12-02T23:06:16Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm Room 911'''<br />
|Andrew Zimmer (LSU)<br />
|[[#Andrew Zimmer (LSU)| "Intrinsic and extrinsic geometries in several complex variables"]]<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Charlotte Chan (MIT)<br />
|[[#Charlotte Chan (MIT)|"Flag varieties and representations of p-adic groups"]]<br />
|Erman<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|<br />
|Soskova/Lempp<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chan (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18516Colloquia/Spring20202019-12-02T21:46:31Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm Room 911'''<br />
|Andrew Zimmer (LSU)<br />
|[[#Andrew Zimmer (LSU)| "Intrinsic and extrinsic geometries in several complex variables"]]<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Charlotte Chan<br />
|Flag varieties and representations of p-adic groups<br />
|Erman<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|<br />
|Soskova/Lempp<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chan (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18499Colloquia/Spring20202019-11-27T18:14:15Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm'''<br />
|Andrew Zimmer<br />
| Intrinsic and extrinsic geometries in several complex variables<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
| [[#Hui Yu (Columbia)| Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|<br />
|Soskova/Lempp<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18472Colloquia/Spring20202019-11-22T21:23:21Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm'''<br />
|Andrew Zimmer<br />
| Intrinsic and extrinsic geometries in several complex variables<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
| <br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18471Colloquia/Spring20202019-11-22T21:18:44Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao<br />
| [[#Tingran Gao| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm'''<br />
|Andrew Zimmer<br />
| Intrinsic and extrinsic geometries in several complex variables<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
| <br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18461Colloquia/Spring20202019-11-21T19:45:31Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 27 '''Monday 4-5 pm'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao<br />
|<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm'''<br />
|Andrew Zimmer<br />
| Intrinsic and extrinsic geometries in several complex variables<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
| <br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18460Colloquia/Spring20202019-11-21T19:37:03Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 27 '''Monday 4-5 pm'''<br />
|Tatyana Shcherbina (Princeton)<br />
|Random matrix theory and supersymmetry techniques<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao<br />
|<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm'''<br />
|Andrew Zimmer<br />
| Intrinsic and extrinsic geometries in several complex variables<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
| <br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18408Colloquia/Spring20202019-11-14T17:26:10Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao<br />
|<br />
|Smith<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18373Colloquia/Spring20202019-11-08T17:39:46Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "TBA"]]<br />
| Kent<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: TBA<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18372Colloquia/Spring20202019-11-08T17:38:12Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|-<br />
|Nov 20 Wednesday<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "TBA"]]<br />
| Kent<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: TBA<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18371Colloquia/Spring20202019-11-08T17:37:28Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|-<br />
|Nov 20 Wednesday<br />
|Franca Hoffman (Caltech)<br />
[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "TBA"]]<br />
| Kent<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: TBA<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18356Colloquia/Spring20202019-11-08T01:32:57Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|-<br />
|Nov 20 Wednesday<br />
|Franca Hoffman<br />
|<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "TBA"]]<br />
| Kent<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: TBA<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18355Colloquia/Spring20202019-11-08T01:32:23Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|-<br />
|Nov 20 Wednesday<br />
|Franca Hoffman<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "TBA"]]<br />
| Kent<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: TBA<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18354Colloquia/Spring20202019-11-08T01:31:33Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|-<br />
|Nov 20 Wednesday<br />
|Franca Hoffman<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "TBA"]]<br />
| Kent<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: TBA<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18353Colloquia/Spring20202019-11-08T01:30:43Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|-<br />
|Nov 20 <br />
|Franca Hoffman<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "TBA"]]<br />
| Kent<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: TBA<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18352Colloquia/Spring20202019-11-08T01:30:04Z<p>Bolotin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|-<br />
|Nov 20 Franca Hoffman<br />
|<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "TBA"]]<br />
| Kent<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: TBA<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=3732PDE Geometric Analysis seminar2012-04-09T22:46:57Z<p>Bolotin: </p>
<hr />
<div>The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
== Seminar Schedule Spring 2012 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb 6<br />
|Yao Yao (UCLA)<br />
|[[#Yao Yao (UCLA)|<br />
Degenerate diffusion with nonlocal aggregation: behavior of solutions]]<br />
|Kiselev<br />
|-<br />
|March 12<br />
| Xuan Hien Nguyen (Iowa State)<br />
|[[#Xuan Hien Nguyen (Iowa State)|<br />
Gluing constructions for solitons and self-shrinkers under mean curvature flow]]<br />
|Angenent<br />
|-<br />
|March 21(Wednesday!), Room 901 Van Vleck<br />
|Nestor Guillen (UCLA)<br />
|[[#Nestor Guillen (UCLA)|<br />
The local geometry of maps with c-convex potentials]]<br />
|Feldman<br />
|-<br />
|March 26<br />
|Vlad Vicol (University of Chicago)<br />
|[[#Vlad Vicol (U Chicago)|<br />
Shape dependent maximum principles and applications]]<br />
|Kiselev<br />
|-<br />
|April 9<br />
|Charles Smart (MIT) <br />
|[[#Charles Smart (MIT)|<br />
PDE methods for the Abelian sandpile<br />
]]<br />
|Seeger<br />
|-<br />
|April 16<br />
|Jiahong Wu (Oklahoma)<br />
|[[#Jiahong Wu (Oklahoma State)|<br />
The 2D Boussinesq equations with partial dissipation]]<br />
|Kiselev<br />
|-<br />
|April 23<br />
|Joana Oliveira dos Santos Amorim (Universite Paris Dauphine)<br />
|[[#Joana Oliveira dos Santos Amorim (Universite Paris Dauphine)|<br />
A geometric look on Aubry-Mather theory and a theorem of Birkhoff]]<br />
|Bolotin<br />
|-<br />
|May 14<br />
|Jacob Glenn-Levin (UT Austin)<br />
|[[#Jacob Glenn-Levin (UT Austin)|<br />
TBA]]<br />
|Kiselev<br />
|}<br />
<br />
==Abstracts==<br />
<br />
===Yao Yao (UCLA)===<br />
''Degenerate diffusion with nonlocal aggregation: behavior of solutions''<br />
<br />
The Patlak-Keller-Segel (PKS) equation models the collective motion of<br />
cells which are attracted by a self-emitted chemical substance. While the<br />
global well-posedness and finite-time blow up criteria are well known, the<br />
asymptotic behaviors of solutions are not completely clear. In this talk I<br />
will present some results on the asymptotic behavior of solutions when<br />
there is global existence. The key tools used in the paper are<br />
maximum-principle type arguments as well as estimates on mass concentration<br />
of solutions. This is a joint work with Inwon Kim.<br />
<br />
===Xuan Hien Nguyen (Iowa State)===<br />
<br />
''Gluing constructions for solitons and self-shrinkers under mean curvature flow''<br />
<br />
In the 1990s, Kapouleas and Traizet constructed new examples of minimal surfaces by desingularizing the intersection of existing ones with Scherk surfaces. Using this idea, one can find new examples of self-translating solutions for the mean curvature flow asymptotic at infinity to a finite family of grim reaper cylinders in general position. Recently, it has been shown that it is possible to desingularize the intersection of a sphere and a plane to obtain a family of self-shrinkers under mean curvature flow. I will discuss the main steps and difficulties for these gluing constructions, as well as open problems.<br />
<br />
===Nestor Guillen (UCLA)===<br />
<br />
We consider the Monge-Kantorovich problem, which consists in<br />
transporting a given measure into another "target" measure in a way<br />
that minimizes the total cost of moving each unit of mass to its new<br />
location. When the transport cost is given by the square of the<br />
distance between two points, the optimal map is given by a convex<br />
potential which solves the Monge-Ampère equation, in general, the<br />
solution is given by what is called a c-convex potential. In recent<br />
work with Jun Kitagawa, we prove local Holder estimates of optimal<br />
transport maps for more general cost functions satisfying a<br />
"synthetic" MTW condition, in particular, the proof does not really<br />
use the C^4 assumption made in all previous works. A similar result<br />
was recently obtained by Figalli, Kim and McCann using different<br />
methods and assuming strict convexity of the target.<br />
<br />
===Charles Smart (MIT)===<br />
<br />
''PDE methods for the Abelian sandpile''<br />
<br />
Abstract: The Abelian sandpile growth model is a deterministic<br />
diffusion process for chips placed on the $d$-dimensional integer<br />
lattice. One of the most striking features of the sandpile is that it<br />
appears to produce terminal configurations converging to a peculiar<br />
lattice. One of the most striking features of the sandpile is that it<br />
appears to produce terminal configurations converging to a peculiar<br />
fractal limit when begun from increasingly large stacks of chips at<br />
the origin. This behavior defied explanation for many years until<br />
viscosity solution theory offered a new perspective. This is joint<br />
work with Lionel Levine and Wesley Pegden.<br />
<br />
===Vlad Vicol (University of Chicago)===<br />
<br />
Title: Shape dependent maximum principles and applications<br />
<br />
Abstract: We present a non-linear lower bound for the fractional Laplacian, when<br />
evaluated at extrema of a function. Applications to the global well-posedness of active<br />
scalar equations arising in fluid dynamics are discussed. This is joint work with P.<br />
Constantin.<br />
<br />
<br />
===Jiahong Wu (Oklahoma State)===<br />
<br />
"The 2D Boussinesq equations with partial dissipation"<br />
<br />
The Boussinesq equations concerned here model geophysical flows such<br />
as atmospheric fronts and ocean circulations. Mathematically the 2D Boussinesq<br />
equations serve as a lower-dimensional model of the 3D hydrodynamics<br />
equations. In fact, the 2D Boussinesq equations retain some key features<br />
of the 3D Euler and the Navier-Stokes equations such as the vortex stretching<br />
mechanism. The global regularity problem on the 2D Boussinesq equations<br />
with partial dissipation has attracted considerable attention in the last few years.<br />
In this talk we will summarize recent results on various cases of partial dissipation,<br />
present the work of Cao and Wu on the 2D Boussinesq equations with vertical<br />
dissipation and vertical thermal diffusion, and explain the work of Chae and Wu on<br />
the critical Boussinesq equations with a logarithmically singular velocity.<br />
<br />
<br />
===Joana Oliveira dos Santos Amorim (Universit\'e Paris Dauphine)===<br />
<br />
"A geometric look on Aubry-Mather theory and a theorem of Birkhoff"<br />
<br />
Given a Tonelli Hamiltonian $H:T^*M \lto \Rm$ in the cotangent bundle of a compact manifold $M$, <br />
we can study its dynamic using the Aubry and Ma\~n\'e sets defined by Mather. <br />
In this talk we will explain their importance and give a new geometric definition <br />
which allows us to understand their property of symplectic invariance. <br />
Moreover, using this geometric definition, we will show that an exact <br />
Lipchitz Lagrangian manifold isotopic to a graph which is invariant <br />
by the flow of a Tonelli Hamiltonian is itself a graph. <br />
This result, in its smooth form, was a conjecture of Birkhoff.<br />
<br />
<br />
===Jacob Glenn-Levin (UT Austin)===<br />
<br />
TBA</div>Bolotinhttps://www.math.wisc.edu/wiki/index.php?title=PDE_Geometric_Analysis_seminar&diff=3731PDE Geometric Analysis seminar2012-04-09T22:43:15Z<p>Bolotin: </p>
<hr />
<div>The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.<br />
<br />
===[[Previous PDE/GA seminars]]===<br />
<br />
== Seminar Schedule Spring 2012 ==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb 6<br />
|Yao Yao (UCLA)<br />
|[[#Yao Yao (UCLA)|<br />
Degenerate diffusion with nonlocal aggregation: behavior of solutions]]<br />
|Kiselev<br />
|-<br />
|March 12<br />
| Xuan Hien Nguyen (Iowa State)<br />
|[[#Xuan Hien Nguyen (Iowa State)|<br />
Gluing constructions for solitons and self-shrinkers under mean curvature flow]]<br />
|Angenent<br />
|-<br />
|March 21(Wednesday!), Room 901 Van Vleck<br />
|Nestor Guillen (UCLA)<br />
|[[#Nestor Guillen (UCLA)|<br />
The local geometry of maps with c-convex potentials]]<br />
|Feldman<br />
|-<br />
|March 26<br />
|Vlad Vicol (University of Chicago)<br />
|[[#Vlad Vicol (U Chicago)|<br />
Shape dependent maximum principles and applications]]<br />
|Kiselev<br />
|-<br />
|April 9<br />
|Charles Smart (MIT) <br />
|[[#Charles Smart (MIT)|<br />
PDE methods for the Abelian sandpile<br />
]]<br />
|Seeger<br />
|-<br />
|April 16<br />
|Jiahong Wu (Oklahoma)<br />
|[[#Jiahong Wu (Oklahoma State)|<br />
The 2D Boussinesq equations with partial dissipation]]<br />
|Kiselev<br />
|-<br />
|April 23<br />
|Joana Oliveira dos Santos Amorim (Universite Paris Dauphine)<br />
|[[#Joana Oliveira dos Santos Amorim (Universite Paris Dauphine)|<br />
A geometric look on Aubry-Mather theory and a theorem of Birkhoff]]<br />
|Bolotin<br />
|-<br />
|May 14<br />
|Jacob Glenn-Levin (UT Austin)<br />
|[[#Jacob Glenn-Levin (UT Austin)|<br />
TBA]]<br />
|Kiselev<br />
|}<br />
<br />
==Abstracts==<br />
<br />
===Yao Yao (UCLA)===<br />
''Degenerate diffusion with nonlocal aggregation: behavior of solutions''<br />
<br />
The Patlak-Keller-Segel (PKS) equation models the collective motion of<br />
cells which are attracted by a self-emitted chemical substance. While the<br />
global well-posedness and finite-time blow up criteria are well known, the<br />
asymptotic behaviors of solutions are not completely clear. In this talk I<br />
will present some results on the asymptotic behavior of solutions when<br />
there is global existence. The key tools used in the paper are<br />
maximum-principle type arguments as well as estimates on mass concentration<br />
of solutions. This is a joint work with Inwon Kim.<br />
<br />
===Xuan Hien Nguyen (Iowa State)===<br />
<br />
''Gluing constructions for solitons and self-shrinkers under mean curvature flow''<br />
<br />
In the 1990s, Kapouleas and Traizet constructed new examples of minimal surfaces by desingularizing the intersection of existing ones with Scherk surfaces. Using this idea, one can find new examples of self-translating solutions for the mean curvature flow asymptotic at infinity to a finite family of grim reaper cylinders in general position. Recently, it has been shown that it is possible to desingularize the intersection of a sphere and a plane to obtain a family of self-shrinkers under mean curvature flow. I will discuss the main steps and difficulties for these gluing constructions, as well as open problems.<br />
<br />
===Nestor Guillen (UCLA)===<br />
<br />
We consider the Monge-Kantorovich problem, which consists in<br />
transporting a given measure into another "target" measure in a way<br />
that minimizes the total cost of moving each unit of mass to its new<br />
location. When the transport cost is given by the square of the<br />
distance between two points, the optimal map is given by a convex<br />
potential which solves the Monge-Ampère equation, in general, the<br />
solution is given by what is called a c-convex potential. In recent<br />
work with Jun Kitagawa, we prove local Holder estimates of optimal<br />
transport maps for more general cost functions satisfying a<br />
"synthetic" MTW condition, in particular, the proof does not really<br />
use the C^4 assumption made in all previous works. A similar result<br />
was recently obtained by Figalli, Kim and McCann using different<br />
methods and assuming strict convexity of the target.<br />
<br />
===Charles Smart (MIT)===<br />
<br />
''PDE methods for the Abelian sandpile''<br />
<br />
Abstract: The Abelian sandpile growth model is a deterministic<br />
diffusion process for chips placed on the $d$-dimensional integer<br />
lattice. One of the most striking features of the sandpile is that it<br />
appears to produce terminal configurations converging to a peculiar<br />
lattice. One of the most striking features of the sandpile is that it<br />
appears to produce terminal configurations converging to a peculiar<br />
fractal limit when begun from increasingly large stacks of chips at<br />
the origin. This behavior defied explanation for many years until<br />
viscosity solution theory offered a new perspective. This is joint<br />
work with Lionel Levine and Wesley Pegden.<br />
<br />
===Vlad Vicol (University of Chicago)===<br />
<br />
Title: Shape dependent maximum principles and applications<br />
<br />
Abstract: We present a non-linear lower bound for the fractional Laplacian, when<br />
evaluated at extrema of a function. Applications to the global well-posedness of active<br />
scalar equations arising in fluid dynamics are discussed. This is joint work with P.<br />
Constantin.<br />
<br />
<br />
===Jiahong Wu (Oklahoma State)===<br />
<br />
"The 2D Boussinesq equations with partial dissipation"<br />
<br />
The Boussinesq equations concerned here model geophysical flows such<br />
as atmospheric fronts and ocean circulations. Mathematically the 2D Boussinesq<br />
equations serve as a lower-dimensional model of the 3D hydrodynamics<br />
equations. In fact, the 2D Boussinesq equations retain some key features<br />
of the 3D Euler and the Navier-Stokes equations such as the vortex stretching<br />
mechanism. The global regularity problem on the 2D Boussinesq equations<br />
with partial dissipation has attracted considerable attention in the last few years.<br />
In this talk we will summarize recent results on various cases of partial dissipation,<br />
present the work of Cao and Wu on the 2D Boussinesq equations with vertical<br />
dissipation and vertical thermal diffusion, and explain the work of Chae and Wu on<br />
the critical Boussinesq equations with a logarithmically singular velocity.<br />
<br />
===Jacob Glenn-Levin (UT Austin)===<br />
<br />
TBA</div>Bolotin