https://hilbert.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Kent&feedformat=atomUW-Math Wiki - User contributions [en]2021-04-18T15:18:41ZUser contributionsMediaWiki 1.30.1https://hilbert.math.wisc.edu/wiki/index.php?title=Dynamics_Seminar_2020-2021&diff=20641Dynamics Seminar 2020-20212021-01-25T00:26:20Z<p>Kent: </p>
<hr />
<div>The [[Dynamics Seminar]] meets virtually on '''Wednesdays''' from '''2:30pm - 3:20pm'''.<br />
<br> <br />
For more information, contact Chenxi Wu.<br />
To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu<br />
<br />
The zoom login info is as follows:<br />
<br />
Join Zoom Meeting<br />
https://uwmadison.zoom.us/j/93164776780?pwd=anE2Y3RhWk1VR0lDa0hnMzhPTTJEUT09<br />
<br />
Meeting ID: 931 6477 6780<br />
Passcode: 819612<br />
<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Spring 2021 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|February 3<br />
|Daniel Woodhouse (Oxford)<br />
|TBA<br />
| <br />
|-<br />
|February 10<br />
|John Mackay (Bristol)<br />
|TBA<br />
| <br />
|-<br />
|February 17<br />
|Benjamin Branman (Wisconsin)<br />
|TBA<br />
| <br />
|-<br />
|February 24<br />
|Uri Bader (Weizmann Institute)<br />
|TBA<br />
| <br />
|-<br />
|March 3<br />
|Omri Sarig (Weizmann Institute)<br />
|TBA<br />
| <br />
|-<br />
|March 10<br />
|Chris Leininger (Rice University)<br />
|TBA<br />
| <br />
|-<br />
|April 28<br />
|Matt Bainbridge (Indiana)<br />
|TBA<br />
|}<br />
<br />
== Fall 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 16<br />
|Andrew Zimmer (Wisconsin)<br />
|An introduction to Anosov representations I<br />
| <br />
|-<br />
|September 23<br />
|Andrew Zimmer (Wisconsin)<br />
|An introduction to Anosov representations II<br />
| <br />
|-<br />
|September 30<br />
|Chenxi Wu (Wisconsin)<br />
|Asymptoic translation lengths on curve complexes and free factor complexes<br />
|<br />
|-<br />
|October 7<br />
|Kathryn Lindsey (Boston College)<br />
|Slices of Thurston's Master Teapot<br />
|<br />
|-<br />
|October 14<br />
|Daniel Thompson (Ohio State)<br />
|Strong ergodic properties for equilibrium states in non-positive curvature<br />
|<br />
|-<br />
|October 21<br />
|Giulio Tiozzo (Toronto)<br />
|Metrics on trees, laminations, and core entropy<br />
| <br />
|-<br />
|October 28<br />
|No talk<br />
|No talk<br />
|<br />
|-<br />
|November 4<br />
|Clark Butler (Princeton)<br />
|"Unbounded uniformizations of Grkmov hyperbolic spaces"<br />
| <br />
|-<br />
|November 11<br />
|Subhadip Dey (Yale)<br />
|Patterson-Sullivan measures for Anosov subgroups<br />
| <br />
|-<br />
|November 18<br />
|Nattalie Tamam (UCSD)<br />
|Effective equidistribution of horospherical flows in infinite volume<br />
| <br />
|-<br />
|November 25<br />
|Tariq Osman (Queens)<br />
|Limit Theorems for Quadratic Weyl Sums<br />
| <br />
|-<br />
|December 2<br />
|Wenyu Pan (Chicago)<br />
|Exponential mixing of geodesic flows for geometrically finite hyperbolic manifolds with cusps<br />
| <br />
|-<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Andrew Zimmer===<br />
<br />
"An introduction to Anosov representations"<br />
<br />
Anosov representations are a special class of representations of finitely generated groups into Lie groups, which are defined using ideas from dynamics (namely, the theory of Anosov flows). In this talk, I will explain the definition (in a special case), give some examples, and describe some properties. I will focus on the case of representations into the general linear group where no background knowledge about Lie groups is required.<br />
<br />
<br />
===Chenxi Wu===<br />
<br />
"Asymptotic translation lengths on curve complexes and free factor complexes"<br />
<br />
The curve complex of a closed surface is a simplicial complex where the vertices are simple closed curves up to isotopy and faces are curves that are disjoint, and an analogy for the curve complex in the setting of Out(F_n) is the free factor complex. A pseudo-Anosov map induces a map from the curve graph to itself, and a basic question is to study the asymptotic translation length which is known to be a non-zero rational number. I will review some prior results on the study of this asymptotic translation length, as well as some of their analogies in the setting of free factor complexes. The latter part is an ongoing project with Hyrungryul Baik and Dongryul Kim. [https://wuchenxi.github.io/graph.pdf Slides]<br />
<br />
<br />
===Kathryn Lindsey===<br />
<br />
"Slices of Thurston's Master Teapot"<br />
<br />
Thurston's Master Teapot is the closure of the set of all points $(z,\lambda) \in \mathbb{C} \times \mathbb{R}$ such that $\lambda$ is the growth rate of a critically periodic unimodal self-map of an interval and $z$ is a Galois conjugate of $\lambda$. I will present a new characterization of which points are in this set. This characterization gives a way to think of each horizontal slice of the Master Teapot as an analogy of the Mandelbrot set for a "restricted iterated function system." An application of this characterization is that the Master Teapot is not invariant under the map $(z,\lambda) \mapsto (-z,\lambda)$. This presentation is based on joint work with Chenxi Wu.<br />
<br />
<br />
===Daniel Thompson===<br />
<br />
"Strong ergodic properties for equilibrium states in non-positive curvature"<br />
<br />
Equilibrium states for geodesic flows over compact rank 1 manifolds and sufficiently regular potential functions were studied by Burns, Climenhaga, Fisher and myself. We showed that if the higher rank set does not carry full topological pressure then the equilibrium state is unique. In this talk, I will describe some recent results on the dynamical properties of these unique equilibrium states. We show that these equilibrium states have the Kolmogorov property (joint with Ben Call), and that approximations of the equilibrium states by regular closed geodesics asymptotically satisfy a type of Central Limit Theorem (joint with Tianyu Wang).<br />
<br />
===Giulio Tiozzo===<br />
<br />
"Metrics on trees, laminations, and core entropy"<br />
<br />
The notion of core entropy, defined as the entropy of the restriction to the Hubbard tree,<br />
was formulated by W. Thurston to produce a combinatorial invariant which captures the topological complexity of polynomial Julia sets and varies in a rich fractal way over parameter space.<br />
<br />
Core entropy has been so far defined by looking at a Markov partition on the tree, or by a combinatorial construction involving infinite graphs. We will introduce a new interpretation of core entropy based on metrics on trees and, dually, on transverse measures on laminations<br />
defining the Julia set.<br />
<br />
On the one hand, this will define a new notion of transverse measures on quadratic laminations, completing the analogy with laminations on surfaces on the “other side” of Sullivan’s dictionary.<br />
Moreover, this is also related to a question of Milnor on a piecewise-linear analogue of Thurston iteration on Teichmueller space.<br />
<br />
===Clark Butler===<br />
<br />
"Unbounded uniformizations of Grkmov hyperbolic spaces"<br />
<br />
In a fundamental work Bonk, Heinonen, and Koskela established a conformal correspondence between Gromov hyperbolic spaces and bounded uniform spaces (satisfying certain additional hypotheses) that generalized the classical conformal correspondence between the Euclidean unit disk and the hyperbolic plane. We prove a similar conformal correspondence between Gromov hyperbolic spaces and unbounded uniform spaces that extends the correspondence between the Euclidean upper half plane and the hyperbolic plane. Our primary application of this uniformization procedure is to extend a number of recent results of Bjorn-Bjorn-Shanmugalingam for Besov spaces on compact metric spaces to Besov spaces on proper metric spaces. These results are derived through a Patterson-Sullivan-esque construction by realizing certain measures on these metric spaces as the boundary values of measures on uniformized Gromov hyperbolic spaces having these metric spaces as their boundaries.<br />
<br />
===Subhadip Dey===<br />
<br />
"Patterson-Sullivan measures for Anosov subgroups"<br />
<br />
Patterson-Sullivan measures were introduced by Patterson (1976) and Sullivan (1979) to study the Kleinian groups and their limit sets. In this talk, we discuss an extension of this classical construction for $P$-Anosov subgroups $\Gamma$ of $G$, where $G$ is a real semisimple Lie group and $P<G$ is a parabolic subgroup. In parallel with the theory for Kleinian groups, we will discuss how one can understand the Hausdorff dimension of the limit set of $\Gamma$ in terms of a certain critical exponent. This is a joint work with Michael Kapovich.<br />
<br />
===Nattalie Tamam===<br />
<br />
"Effective equidistribution of horospherical flows in infinite volume"<br />
<br />
Horospherical flows in homogeneous spaces have been studied intensively over the last several decades and have many surprising applications in various fields. Many basic results are under the assumption that the volume of the space is finite, which is crucial as many basic ergodic theorems fail in the setting of an infinite measure space.In the talk we will discuss the infinite volume setting, and specifically, when can we expect horospherical orbits to equidistribute. Our goal will be to provide an effective equidistribution result, with polynomial rate, for horospherical orbits in the frame bundle of certain infinite volume hyperbolic manifolds. This is a joint work with Jacqueline Warren.<br />
<br />
===Tariq Osman===<br />
<br />
"Limit Theorems for Quadratic Weyl Sums"<br />
<br />
Consider exponential sums of the form $S_N(x, \alpha) := \sum_{n = 1}^{N}e(1/2 n^2 x + n\alpha)$, known as quadratic Weyl sums. We will use homogeneous dynamics to establish a limiting distribution for $\frac{1}{\sqrt N} |S_N(x, \alpha)|$, when $\alpha$ is a fixed rational, and $x$ is chosen uniformly from the unit interval. Time permitting, we will study the tails of the limiting distribution to show that this is not the central limit theorem in disguise. (This is joint work with Francesco Cellarosi)<br />
<br />
===Wenyu Pan===<br />
<br />
"Exponential mixing of geodesic flows for geometrically finite hyperbolic manifolds with cusps"<br />
<br />
Let $\mathbb{H}^n$ be the hyperbolic $n$-space and $\Gamma$ be a geometrically finite discrete subgroup in $\operatorname{Isom}_{+}(\mathbb{H}^n)$ with parabolic elements. In the joint work with Jialun LI, we establish exponential mixing of the geodesic flow over the unit tangent bundle $T^1(\Gamma\backslash \mathbb{H}^n)$ with respect to the Bowen-Margulis-Sullivan measure. Our approach is to construct coding for the geodesic flow and then prove a Dolgopyat-type spectral estimate for the corresponding transfer operator. In the talk, I am planning to explain the construction of the coding. I will also discuss the application of obtaining a resonance-free region for the resolvent on $\Gamma\backslash \mathbb{H}^n$.</div>Kenthttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18397Colloquia/Spring20202019-11-11T20:43:45Z<p>Kent: </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 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>Kenthttps://hilbert.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=18233Colloquia/Spring20202019-10-23T02:34:34Z<p>Kent: </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 />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<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 />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: TBA<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>Kenthttps://hilbert.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=16196Geometry and Topology Seminar 2019-20202018-10-14T04:06:20Z<p>Kent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 14<br />
|Teddy Einstein (UIC)<br />
|Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes<br />
|(Dymarz)<br />
|-<br />
|Oct. 12<br />
|Marissa Loving <br />
|Least dilatation of pure surface braids<br />
|(Kent)<br />
|-<br />
|Oct. 19<br />
|Sara Maloni <br />
|On type-preserving representations of thrice punctured projective plane group<br />
|(Kent)<br />
|-<br />
|Oct. 26<br />
|Dingxin Zhang (Harvard-CMSA)<br />
|Relative cohomology and A-hypergeometric equations<br />
|(Huang)<br />
|-<br />
|Nov. 9<br />
|Zhongshan An (Stony Brook)<br />
|Ellipticity of the Bartnik Boundary Conditions<br />
|(Huang)<br />
|-<br />
|Nov. 16<br />
|Xiangdong Xie<br />
|TBA<br />
|(Dymarz)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Teddy Einstein===<br />
<br />
"Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes"<br />
<br />
Non-positively curved (NPC) cube complexes are important tools in low dimensional topology and group theory and play a prominent role in Agol's proof of the Virtual Haken Conjecture. Constructing a hierarchy for a NPC cube complex is a powerful method of decomposing its fundamental group essential to the theory of NPC cube complex theory. When a cube complex admits a hierarchy with nice properties, it becomes possible to use the hierarchy structure to make inductive arguments. I will explain what a quasiconvex hierarchy of an NPC cube complex is and briefly discuss some of the applications. We will see an outline of how to construct a quasiconvex hierarchy for a relatively hyperbolic NPC cube complex and some of the hyperbolic and relatively hyperbolic geometric tools used to ensure the hierarchy is indeed quasiconvex.<br />
<br />
===Marissa Loving===<br />
<br />
"Least dilatation of pure surface braids"<br />
<br />
The n-stranded pure surface braid group of a genus g surface can be described as the subgroup of the pure mapping class group of a surface of genus g with n-punctures which becomes trivial on the closed surface. I am interested in the least dilatation of pseudo-Anosov pure surface braids. For the n=1 case, upper and lower bounds on the least dilatation were proved by Dowdall and Aougab—Taylor, respectively. In this talk, I will describe the upper and lower bounds I have proved as a function of g and n.<br />
<br />
===Sara Maloni===<br />
<br />
"On type-preserving representations of thrice punctured projective plane group"<br />
<br />
In this talk, after a brief overview on famous topological and dynamical open questions on character varieties, we will consider type-preserving representations of the fundamental group of the three-holed projective plane N into PGL(2, R). First, we prove Kashaev’s conjecture on the number of connected components with non-maximal euler class. Second, we show that for all representations with euler class 0 there is a one simple closed curve which is sent to a non-hyperbolic element, while in euler class 1 or -1 we show that there are six components where all the simple closed curves are sent to hyperbolic elements and 2 components where there are some simple closed curves sent to non-hyperbolic elements. This answers a generalisation of a question asked by Bowditch for orientable surfaces. In addition, we show, in most cases, that the action of the pure mapping class group Mod(N) on these non-maximal components is ergodic, proving Goldman conjecture in those cases. Time permitting we will discuss a work in progress with Palesi where we expend these results to all five surfaces (orientable and non-orientable) of characteristic -2. (This is joint work with F. Palesi and T. Yang.)<br />
<br />
===Dingxin Zhang===<br />
"Relative cohomology and A-hypergeometric equations"<br />
<br />
The GKZ hypergeometric equations are closely related to the period integrals of algebraic varieties. Based on the theorems of Walther--Schulze, we identify the set of solutions of a certain GKZ system with some relative homology groups. Our result generalizes the theorem of Huang--Lian--Yau--Zhu. This is a joint work with Tsung-Ju Lee.<br />
<br />
<br />
===Zhongshan An===<br />
"Ellipticity of the Bartnik Boundary Conditions"<br />
<br />
The Bartnik quasi-local mass is defined to measure the mass of a bounded manifold with boundary, where a collection of geometric boundary data — the so-called Bartnik boundary data— plays a key role. Bartnik proposed the open problem whether, on a given manifold with boundary, there exists a stationary vacuum metric so that the Bartnik boundary conditions are realized. In the effort to answer this question, it is important to prove the ellipticity of Bartnik boundary conditions for stationary vacuum metrics. In this talk, I will start with an introduction to the Bartnik quasi-local mass and the moduli space of stationary vacuum metrics. Then I will explain the ellipticity result for the Bartnik boundary conditions and, as an application, give a partial answer to the existence question. <br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
2017-2018 [[Geometry_and_Topology_Seminar_2017-2018]]<br />
<br><br><br />
2016-2017 [[Geometry_and_Topology_Seminar_2016-2017]]<br />
<br><br><br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kenthttps://hilbert.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=16195Geometry and Topology Seminar 2019-20202018-10-14T04:05:28Z<p>Kent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 14<br />
|Teddy Einstein (UIC)<br />
|Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes<br />
|(Dymarz)<br />
|-<br />
|Oct. 12<br />
|Marissa Loving <br />
|Least dilatation of pure surface braids<br />
|(Kent)<br />
|-<br />
|Oct. 19<br />
|Sara Maloni <br />
|TBA<br />
|(Kent)<br />
|-<br />
|Oct. 26<br />
|Dingxin Zhang (Harvard-CMSA)<br />
|Relative cohomology and A-hypergeometric equations<br />
|(Huang)<br />
|-<br />
|Nov. 9<br />
|Zhongshan An (Stony Brook)<br />
|Ellipticity of the Bartnik Boundary Conditions<br />
|(Huang)<br />
|-<br />
|Nov. 16<br />
|Xiangdong Xie<br />
|TBA<br />
|(Dymarz)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Teddy Einstein===<br />
<br />
"Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes"<br />
<br />
Non-positively curved (NPC) cube complexes are important tools in low dimensional topology and group theory and play a prominent role in Agol's proof of the Virtual Haken Conjecture. Constructing a hierarchy for a NPC cube complex is a powerful method of decomposing its fundamental group essential to the theory of NPC cube complex theory. When a cube complex admits a hierarchy with nice properties, it becomes possible to use the hierarchy structure to make inductive arguments. I will explain what a quasiconvex hierarchy of an NPC cube complex is and briefly discuss some of the applications. We will see an outline of how to construct a quasiconvex hierarchy for a relatively hyperbolic NPC cube complex and some of the hyperbolic and relatively hyperbolic geometric tools used to ensure the hierarchy is indeed quasiconvex.<br />
<br />
===Marissa Loving===<br />
<br />
"Least dilatation of pure surface braids"<br />
<br />
The n-stranded pure surface braid group of a genus g surface can be described as the subgroup of the pure mapping class group of a surface of genus g with n-punctures which becomes trivial on the closed surface. I am interested in the least dilatation of pseudo-Anosov pure surface braids. For the n=1 case, upper and lower bounds on the least dilatation were proved by Dowdall and Aougab—Taylor, respectively. In this talk, I will describe the upper and lower bounds I have proved as a function of g and n.<br />
<br />
===Sara Maloni===<br />
<br />
"On type-preserving representations of thrice punctured projective plane group"<br />
<br />
In this talk, after a brief overview on famous topological and dynamical open questions on character varieties, we will consider type-preserving representations of the fundamental group of the three-holed projective plane N into PGL(2, R). First, we prove Kashaev’s conjecture on the number of connected components with non-maximal euler class. Second, we show that for all representations with euler class 0 there is a one simple closed curve which is sent to a non-hyperbolic element, while in euler class 1 or -1 we show that there are six components where all the simple closed curves are sent to hyperbolic elements and 2 components where there are some simple closed curves sent to non-hyperbolic elements. This answers a generalisation of a question asked by Bowditch for orientable surfaces. In addition, we show, in most cases, that the action of the pure mapping class group Mod(N) on these non-maximal components is ergodic, proving Goldman conjecture in those cases. Time permitting we will discuss a work in progress with Palesi where we expend these results to all five surfaces (orientable and non-orientable) of characteristic -2. (This is joint work with F. Palesi and T. Yang.)<br />
<br />
===Dingxin Zhang===<br />
"Relative cohomology and A-hypergeometric equations"<br />
<br />
The GKZ hypergeometric equations are closely related to the period integrals of algebraic varieties. Based on the theorems of Walther--Schulze, we identify the set of solutions of a certain GKZ system with some relative homology groups. Our result generalizes the theorem of Huang--Lian--Yau--Zhu. This is a joint work with Tsung-Ju Lee.<br />
<br />
<br />
===Zhongshan An===<br />
"Ellipticity of the Bartnik Boundary Conditions"<br />
<br />
The Bartnik quasi-local mass is defined to measure the mass of a bounded manifold with boundary, where a collection of geometric boundary data — the so-called Bartnik boundary data— plays a key role. Bartnik proposed the open problem whether, on a given manifold with boundary, there exists a stationary vacuum metric so that the Bartnik boundary conditions are realized. In the effort to answer this question, it is important to prove the ellipticity of Bartnik boundary conditions for stationary vacuum metrics. In this talk, I will start with an introduction to the Bartnik quasi-local mass and the moduli space of stationary vacuum metrics. Then I will explain the ellipticity result for the Bartnik boundary conditions and, as an application, give a partial answer to the existence question. <br />
<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
2017-2018 [[Geometry_and_Topology_Seminar_2017-2018]]<br />
<br><br><br />
2016-2017 [[Geometry_and_Topology_Seminar_2016-2017]]<br />
<br><br><br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kenthttps://hilbert.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=15688Geometry and Topology Seminar 2019-20202018-08-13T17:35:51Z<p>Kent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 28<br />
|Sara Maloni <br />
|TBA<br />
|(Kent)<br />
|-<br />
|Oct. 12<br />
|Marissa Loving <br />
|TBA<br />
|(Kent)<br />
|-<br />
|Nov. 16<br />
|Xiangdong Xie<br />
|TBA<br />
|(Dymarz)<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== TBA ===<br />
<br />
<br />
== Archive of past Geometry seminars ==<br />
2017-2018 [[Geometry_and_Topology_Seminar_2017-2018]]<br />
<br><br><br />
2016-2017 [[Geometry_and_Topology_Seminar_2016-2017]]<br />
<br><br><br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kenthttps://hilbert.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=12977Geometry and Topology Seminar 2019-20202017-01-14T04:33:47Z<p>Kent: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
== Fall 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 9<br />
| [http://www.math.wisc.edu/~bwang/ Bing Wang] (UW Madison)<br />
| [[#Bing Wang| "The extension problem of the mean curvature flow"]]<br />
| (Local)<br />
|-<br />
|September 16<br />
| [http://www.math.northwestern.edu/~weinkove/ Ben Weinkove] (Northwestern University)<br />
| [[#Ben Weinkove| "Gauduchon metrics with prescribed volume form"]]<br />
| Lu Wang<br />
|-<br />
|September 23<br />
| Jiyuan Han (UW Madison)<br />
| [[#Jiyuan Han| "Deformation theory of scalar-flat ALE Kahler surfaces"]]<br />
| (Local)<br />
|-<br />
|September 30<br />
| <br />
| <br />
|<br />
|-<br />
|October 7<br />
| Yu Li (UW Madison) <br />
| [[#Yu Li| "Ricci flow on asymptotically Euclidean manifolds"]]<br />
| (Local)<br />
|-<br />
|October 14<br />
| [http://math.uchicago.edu/~seanpkh/ Sean Howe] (University of Chicago)<br />
| [[#Sean Howe| "Representation stability and hypersurface sections"]]<br />
| Melanie Matchett Wood<br />
|-<br />
|October 21<br />
| [https://sites.google.com/site/mathnanli/ Nan Li] (CUNY) <br />
| [[#Nan Li| "Quantitative estimates on the singular Sets of Alexandrov spaces"]]<br />
| Lu Wang<br />
|-<br />
|October 28<br />
| Ronan Conlon(Florida International University)<br />
| [[#Ronan Conlon| "New examples of gradient expanding K\"ahler-Ricci solitons"]]<br />
| Bing Wang<br />
|-<br />
|November 4<br />
| Jonathan Zhu (Harvard University)<br />
| [[#Jonathan Zhu| "Entropy and self-shrinkers of the mean curvature flow"]]<br />
| Lu Wang<br />
|-<br />
|November 11<br />
| Canceled.<br />
| <br />
| <br />
|-<br />
|November 18<br />
| [http://www.math.uiuc.edu/~cuyanik2/ Caglar Uyanik] (Illinois)<br />
| [[#Caglar Uyanik| "Geometry and dynamics of free group automorphisms"]]<br />
| [http://www.math.wisc.edu/~rkent Kent]<br />
|- <br />
| Thanksgiving Recess<br />
| <br />
| <br />
|<br />
|-<br />
|December 2<br />
|Peyman Morteza (UW Madison)<br />
| [[#Peyman Morteza| "Gluing construction of Einstein manifolds"]]<br />
| (Local) <br />
|-<br />
|December 9<br />
| Yu Zeng(University of Rochester)<br />
| [[#Yu Zeng| "Short time existence of the Calabi flow with rough initial data"]]<br />
| Bing Wang<br />
| <br />
|-<br />
|December 16<br />
|(No seminar)<br />
| <br />
|-<br />
|<br />
|}<br />
<br />
== Spring 2017 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 20<br />
| [http://people.mpim-bonn.mpg.de/rovi/ Carmen Rovi] (University of Indiana Bloomington)<br />
| [[#Carmen Rovi| "The mod 8 signature of a fiber bundle"]]<br />
| Maxim<br />
|-<br />
|Jan 27<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 3<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 10<br />
| <br />
| <br />
| <br />
|-<br />
|Feb 17<br />
|[http://www.math.northwestern.edu/~hartman/ Yair Hartman] (Northwestern University) <br />
|[[#Yair Hartman| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|Feb 24<br />
| <br />
| <br />
| <br />
|-<br />
|March 3<br />
| [http://www.math.uqam.ca/~powell/ Mark Powell] (Université du Québec à Montréal)<br />
| [[#Mark Powell| "TBA"]]<br />
| Kjuchukova<br />
|-<br />
|March 10<br />
| [http://www.math.wisc.edu/~kent Autumn Kent] (Wisconsin)<br />
| [[#Autumn Kent | ''Analytic functions from hyperbolic manifolds'']]<br />
| local<br />
|-<br />
|March 17<br />
| <br />
| <br />
| <br />
|-<br />
|March 24<br />
| Spring Break<br />
| <br />
| <br />
|-<br />
|March 31<br />
| <br />
| <br />
| <br />
|-<br />
|April 7<br />
| <br />
| <br />
| <br />
|-<br />
|April 14<br />
| <br />
| <br />
| <br />
|-<br />
|April 21<br />
|[http://www.math.csi.cuny.edu/~maher/ Joseph Maher] (CUNY) <br />
| [[#Joseph Maher|"TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|April 28<br />
| [http://bena-tshishiku.squarespace.com/ Bena Tshishiku] (Harvard)<br />
| [[#Bena Tshishiku| "TBA"]]<br />
| [http://www.math.wisc.edu/~dymarz Dymarz]<br />
|-<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
=== Ronan Conlon ===<br />
''New examples of gradient expanding K\"ahler-Ricci solitons''<br />
<br />
A complete K\"ahler metric $g$ on a K\"ahler manifold $M$ is a \emph{gradient expanding K\"ahler-Ricci soliton} if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla^{g}f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+g=0$. I will present new examples of such metrics on the total space of certain holomorphic vector bundles. This is joint work with Alix Deruelle (Universit\'e Paris-Sud).<br />
<br />
<br />
=== Jiyuan Han ===<br />
''Deformation theory of scalar-flat ALE Kahler surfaces''<br />
<br />
We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kahler surfaces. This is used to prove that for any scalar-flat Kahler ALE surfaces, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics is then constructed, which is shown to be universal up to small diffeomorphisms (that is, diffeomorphisms which are close to the identity in a suitable sense). A formula for the dimension of the local moduli space is proved in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of \C^2/\Gamma, where \Gamma is a finite subgroup of U(2) without complex reflections. This is a joint work with Jeff Viaclovsky.<br />
<br />
=== Sean Howe ===<br />
''Representation stability and hypersurface sections''<br />
<br />
We give stability results for the cohomology of natural local systems on spaces of smooth hypersurface sections as the degree goes to \infty. These results give new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. The stabilization occurs in point-counting and in the Grothendieck ring of Hodge structures, and we give explicit formulas for the limits using a probabilistic interpretation. These results have natural geometric analogs -- for example, we show that the "average" smooth hypersurface in \mathbb{P}^n is \mathbb{P}^{n-1}! <br />
<br />
=== Nan Li ===<br />
''Quantitative estimates on the singular sets of Alexandrov spaces''<br />
<br />
The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such structure is sharp in some sense. This is a joint work with Aaron Naber. <br />
<br />
=== Yu Li ===<br />
<br />
In this talk, we prove that if an asymptotically Euclidean (AE) manifold with nonnegative scalar curvature has long time existence of Ricci flow, it converges to the Euclidean space in the strong sense. By convergence, the mass will drop to zero as time tends to infinity. Moreover, in three dimensional case, we use Ricci flow with surgery to give an independent proof of positive mass theorem. A classification of diffeomorphism types is also given for all AE 3-manifolds with nonnegative scalar curvature. <br />
<br />
=== Peyman Morteza ===<br />
''We develop a procedure to construct Einstein metrics by gluing the Calabi metric to an Einstein orbifold. We show that our gluing problem is obstructed and we calculate the obstruction explicitly. When our obstruction does not vanish, we obtain a non-existence result in the case that the base orbifold is compact. When our obstruction vanishes and the base orbifold is non-degenerate and asymptotically hyperbolic we prove an existence result. This is a joint work with Jeff Viaclovsky. ''<br />
<br />
=== Caglar Uyanik ===<br />
''Geometry and dynamics of free group automorphisms''<br />
<br />
A common theme in geometric group theory is to obtain structural results about infinite groups by analyzing their action on metric spaces. In this talk, I will focus on two geometrically significant groups; mapping class groups and outer automorphism groups of free groups.We will describe a particular instance of how the dynamics and geometry of their actions on various spaces provide deeper information about the groups.<br />
<br />
=== Bing Wang ===<br />
''The extension problem of the mean curvature flow''<br />
<br />
We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.<br />
A key ingredient of the proof is to show a two-sided pseudo-locality property of the mean curvature flow, whenever the mean curvature is bounded.<br />
This is a joint work with Haozhao Li.<br />
<br />
=== Ben Weinkove ===<br />
''Gauduchon metrics with prescribed volume form''<br />
<br />
Every compact complex manifold admits a Gauduchon metric in each conformal class of Hermitian metrics. In 1984 Gauduchon conjectured that one can prescribe the volume form of such a metric. I will discuss the proof of this conjecture, which amounts to solving a nonlinear Monge-Ampere type equation. This is a joint work with Gabor Szekelyhidi and Valentino Tosatti.<br />
<br />
=== Jonathan Zhu ===<br />
''Entropy and self-shrinkers of the mean curvature flow''<br />
<br />
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.<br />
<br />
===Yu Zeng===<br />
''Short time existence of the Calabi flow with rough initial data''<br />
<br />
Calabi flow was introduced by Calabi back in 1950’s as a geometric flow approach to the existence of extremal metrics. Analytically it is a fourth order nonlinear parabolic equation on the Kaehler potentials which deforms the Kaehler potential along its scalar curvature. In this talk, we will show that the Calabi flow admits short time solution for any continuous initial Kaehler metric. This is a joint work with Weiyong He.<br />
<br />
== Spring Abstracts ==<br />
<br />
===Carmen Rovi===<br />
''The mod 8 signature of a fiber bundle''<br />
<br />
In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.<br />
<br />
===Bena Tshishiku===<br />
"TBA"<br />
<br />
===Autumn Kent===<br />
''Analytic functions from hyperbolic manifolds''<br />
<br />
At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas involved form a mix of geometry, algebra, and analysis.<br />
<br />
== Archive of past Geometry seminars ==<br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Kenthttps://hilbert.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology&diff=12976Geometry and Topology2017-01-14T04:21:08Z<p>Kent: </p>
<hr />
<div>=='''Seminars'''==<br />
<br />
<b><font size="3">[[Geometry and Topology Seminar]]</font></b><br />
<br />
[[PDE Geometric Analysis seminar]]<br />
<br />
[[Symplectic Geometry Seminar]]<br />
<br />
== '''Faculty''' ==<br />
<br />
'''Faculty in Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~dymarz/ Tullia Dymarz] (U Chicago 2007) Geometric group theory, quasi-isometric rigidity.<br />
<br />
[http://www.math.wisc.edu/~kent Autumn Kent] (UT Austin 2006) <br />
Hyperbolic geometry, mapping class groups, geometric group theory, connections to algebra.<br />
<br />
[http://www.math.wisc.edu/~maribeff/ Gloria Mari-Beffa] (U Minnesota &ndash; Minneapolis 1991) <br />
Differential geometry, invariant theory, completely integrable systems.<br />
<br />
[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim] (U Penn 2005)<br />
Geometry and topology of singularities.<br />
<br />
[http://www.math.wisc.edu/~stpaul/ Sean T. Paul] (Princeton 2000)<br />
Complex differential geometry.<br />
<br />
[http://www.math.wisc.edu/~jeffv/ Jeff Viaclovsky] (Princeton 1999)<br />
Differential geometry, geometric analysis.<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW &ndash; Madison 2008) <br />
Geometric flows.<br />
<br />
[http://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT 2011) <br />
Geometric partial differential equations.<br />
<br />
<br />
'''Faculty with research tied to Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~angenent/ Sigurd Angenent] (Leiden 1986) Partial differential equations.<br />
<br />
[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru] (Cornell 2000) Algebraic geometry, homological algebra, string theory.<br />
<br />
[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.<br />
<br />
[http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] (UT Austin 1998) Fluid dynamics, mixing, biological swimming and mixing, topological dynamics.<br />
<br />
<br />
'''Postdoctoral faculty in Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~villa/ Manuel Gonz&aacute;lez Villa] (Universidad Complutense de<br />
Madrid 2010)<br />
Geometry and topology of singularities of complex algebraic varieties. <br />
<br />
<br />
'''Honorary Fellow'''<br />
<br />
Morris Hirsch (U Chicago 1958)<br />
<br />
<br />
'''Emeriti'''<br />
<br />
Edward Fadell (Ohio State 1952)<br />
<br />
Sufiàn Husseini (Princeton 1960)<br />
Algebraic topology and applications.<br />
<br />
[http://www.math.wisc.edu/~robbin/ Joel Robbin] (Princeton 1965)<br />
Dynamical systems and symplectic geometry.<br />
<br />
Peter Orlik (U Michigan 1966)<br />
<br />
Mary Ellen Rudin (UT Austin 1949)<br />
<br />
<br />
=='''Conferences'''==<br />
<br />
'''Upcoming conferences in Geometry and Topology held at UW'''<br />
<br />
[http://www.math.wisc.edu/~rkent/MXRI.html Moduli Crossroads Retreat, I]<br />
<br />
'''Previous conferences in Geometry and Topology held at UW'''<br />
<br />
[http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
<br />
[https://sites.google.com/site/gtntd2013/ Group Theory, Number Theory, and Topology Day]<br />
<br />
[https://sites.google.com/site/mirrorsymmetryinthemidwest/home Mirror Symmetry in the Midwest II]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing12.html Singularities in the Midwest, II]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing10.html Singularities in the Midwest]<br />
<br />
[http://www.math.wisc.edu/~oh/glgc/ 2010 Great Lakes Geometry Conference]<br />
<br />
<br />
<!-- ''Graduate study in Geometry and Topology at UW-Madison''' --></div>Kent