Difference between revisions of "Colloquia"

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All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.
 
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.
  
==Spring 2019==
 
  
 +
 +
==Fall 2019==
 
{| cellpadding="8"
 
{| cellpadding="8"
 
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!align="left" | host(s)
 
!align="left" | host(s)
 
|-
 
|-
|Jan 25 '''Room 911'''
+
|Sept 6 '''Room 911'''
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW
+
| Will Sawin (Columbia)
|[[#Beata Randrianantoanina (Miami University Ohio) | Some nonlinear problems in the geometry of Banach spaces and their applications  ]]
+
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]
| Tullia Dymarz
+
| Marshall
|
 
 
|-
 
|-
|Jan 30 '''Wednesday'''
+
|Sept 13
| Talk rescheduled to Feb 15
+
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)
 +
|[[#Yan Soibelman (Kansas State)|  Riemann-Hilbert correspondence and Fukaya categories ]]
 +
| Caldararu
 
|
 
|
 
|-
 
|-
|Jan 31 '''Thursday'''
+
|Sept 16 '''Monday Room 911'''
| Talk rescheduled to Feb 13
+
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)
 +
|[[#Alicia Dickenstein (Buenos Aires)|  Algebra and geometry in the study of enzymatic cascades ]]
 +
| Craciun
 
|
 
|
 
|-
 
|-
|Feb 1
+
|Sept 20
| Talk cancelled due to weather
+
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)
|
+
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]
|  
+
| Qin
 
|
 
|
 
|-
 
|-
|Feb 5 '''Tuesday, VV 911'''
+
|Sept 26 '''Thursday 3-4 pm Room 911'''
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)
+
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)
|[[#Alexei Poltoratski (Texas A&M)| Completeness of exponentials: Beurling-Malliavin and type problems  ]]
+
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]
| Denisov
+
| Marshall / Friends of UW Madison Libraries
 
|
 
|
 
|-
 
|-
|Feb 6 '''Wednesday, room 911'''
+
|Sept 27
| [https://lc-tsai.github.io/ Li-Cheng Tsai] (Columbia University)
+
| Omer Mermelstein (Madison)
|[[#Li-Cheng Tsai (Columbia University)| When particle systems meet PDEs  ]]
+
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]
| Anderson
+
|Andrews
|
 
 
|-
 
|-
|Feb 8
+
|Oct 4
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)
 
|[[#Aaron Naber (Northwestern) |  A structure theory for spaces with lower Ricci curvature bounds  ]]
 
| Street
 
 
|
 
|
|-
 
|Feb 11 '''Monday'''
 
| [https://www2.bc.edu/david-treumann/materials.html David Treumann] (Boston College)
 
|[[#David Treumann (Boston College) |  Twisting things in topology and symplectic topology by pth powers  ]]
 
| Caldararu
 
 
|
 
|
 
|-
 
|-
| Feb 13 '''Wednesday'''
+
|Oct 11
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)
 
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations  ]]
 
| Street
 
 
 
|-
 
| Feb 15
 
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)
 
| [[#Lillian Pierce (Duke University) |  Short character sums  ]]
 
| Boston and Street
 
 
|
 
|
|-
 
|Feb 22
 
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)
 
|[[#Angelica Cueto (The Ohio State University)|  Lines on cubic surfaces in the tropics  ]]
 
| Erman and Corey
 
 
|
 
|
 
|-
 
|-
|March 4 '''Monday'''
+
|Oct 18
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota)
+
| Shamgar Gurevich (Madison)
|[[#Vladimir Sverak (Minnesota) | Wasow lecture "PDE aspects of the Navier-Stokes equations and simpler models" ]]
+
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]
| Kim
+
| Marshall
|
 
 
|-
 
|-
|March 8
+
|Oct 25
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)
 
|[[#Jason McCullough (Iowa State)|  On the degrees and complexity of algebraic varieties  ]]
 
| Erman
 
 
|
 
|
 
|-
 
|-
|March 15
+
|Nov 1
| <s>[http://www.its.caltech.edu/~maksym/ Maksym Radziwill] (Caltech)</s> <b>Talk cancelled</b>
+
|Elchanan Mossel (MIT)
|[[#Maksym Radziwill (Caltech) |  <s>Recent progress in multiplicative number theory</s>  ]]
+
|Distinguished Lecture
| Marshall
+
|Roch
|
 
 
|-
 
|-
|March 29
+
|Nov 8
| Jennifer Park (OSU)
+
|Reserved for job talk
|[[#Jennifer Park (OSU) | Rational points on varieties  ]]
 
| Marshall
 
 
|
 
|
 
|-
 
|-
|April 5
+
|Nov 15
| Ju-Lee Kim (MIT)
+
|Reserved for job talk
|[[#Ju-Lee Kim (MIT) |  Types and counting automorphic forms  ]]
 
| Gurevich
 
 
|
 
|
 
|-
 
|-
|April 12
+
|Nov 22
| Eviatar Procaccia (TAMU)
+
|Reserved for job talk
|[[#Eviatar Procaccia |  Can one hear the shape of a random walk?  ]]
 
| Gurevich
 
 
|
 
|
 
|-
 
|-
|April 19
+
|Nov 29
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)
+
|Thanksgiving
|[[#Jo Nelson (Rice)| Contact Invariants and Reeb Dynamics ]]
 
| Jean-Luc
 
 
|
 
|
 
|-
 
|-
|April 22 '''Monday'''
+
|Dec 6
| [https://justinh.su Justin Hsu] (Madison)
+
|Reserved for job talk
|[[#Justin Hsu (Madison) |  From Couplings to Probabilistic Relational Program Logics ]]
 
| Lempp
 
 
|
 
|
 
|-
 
|-
|April 26 '''Room 911'''
+
|Dec 11 '''Wednesday'''
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)
+
|Nick Higham (Manchester)
|[[# Kavita Ramanan (Brown) |  Tales of Random Projections  ]]
+
|LAA lecture
| WIMAW
+
|Brualdi
 
|
 
|
 
|-
 
|-
|May 3
+
|Dec 13
| Tomasz Przebinda (Oklahoma)
+
|Reserved for job talk
|[[# TBA|  TBA  ]]
 
| Gurevich
 
 
|
 
|
 
|}
 
|}
  
 +
==Spring 2020==
  
 
 
 
 
==FALL 2019==
 
 
{| cellpadding="8"
 
{| cellpadding="8"
 
!align="left" | date   
 
!align="left" | date   
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!align="left" | title
 
!align="left" | title
 
!align="left" | host(s)
 
!align="left" | host(s)
 +
|
 
|-
 
|-
|Sept 6
+
|Jan 24
|
+
|Reserved for job talk
 
|
 
|
 
|-
 
|-
|Sept 13
+
|Jan 31
| Jan Soibelman (Kansas State)
+
|Reserved for job talk
|[[# TBA|  TBA  ]]
 
| Caldararu
 
 
|
 
|
 
|-
 
|-
|Sept 16 '''Monday Room 911'''
+
|Feb 7
| Alicia Dickenstein (Buenos Aires)
+
|Reserved for job talk
|[[# TBA|  TBA  ]]
 
| Craciun
 
 
|
 
|
 
|-
 
|-
|Sept 20
+
|Feb 14
 +
|Reserved for job talk
 
|
 
|
 
|-
 
|-
|Sept 27
+
|Feb 21
 +
|Shai Evra (IAS)
 
|
 
|
|-
+
|Gurevich
|Oct 4
 
 
|
 
|
 
|-
 
|-
|Oct 11
+
|Feb 28
 +
|Brett Wick (Washington University, St. Louis)
 
|
 
|
 +
|Seeger
 
|-
 
|-
|Oct 18
+
|March 6
 +
| Jessica Fintzen (Michigan)
 
|
 
|
 +
|Marshall
 
|-
 
|-
|Oct 25
+
|March 13
 
|
 
|
 
|-
 
|-
|Nov 1
+
|March 20
 +
|Spring break
 
|
 
|
 
|-
 
|-
|Nov 8
+
|March 27
|Reserved for job talk
+
|(Moduli Spaces Conference)
 
|
 
|
 +
|Boggess, Sankar
 
|-
 
|-
|Nov 15
+
|April 3
|Reserved for job talk
+
|Caroline Turnage-Butterbaugh (Carleton College)
 
|
 
|
 +
|Marshall
 
|-
 
|-
|Nov 22
+
|April 10
|Reserved for job talk
+
| Sarah Koch (Michigan)
 
|
 
|
 +
| Bruce (WIMAW)
 
|-
 
|-
|Nov 29
+
|April 17
|Thanksgiving
+
|Song Sun (Berkeley)
 
|
 
|
 +
|Huang
 
|-
 
|-
|Dec 6
+
|April 24
|Reserved for job talk
+
|Natasa Sesum (Rutgers University)
 
|
 
|
 +
|Angenent
 
|-
 
|-
|Dec 13
+
|May 1
|Reserved for job talk
+
|Robert Lazarsfeld (Stony Brook)
|
+
|Distinguished lecture
 +
|Erman
 
|}
 
|}
 
 
  
 
== Abstracts ==
 
== Abstracts ==
  
===Beata Randrianantoanina (Miami University Ohio)===
 
 
Title: Some nonlinear problems in the geometry of Banach spaces and their applications.
 
 
Abstract: Nonlinear problems in the geometry of Banach spaces have been studied since the inception of the field. In this talk I will outline some of the history, some of modern applications, and some open directions of research. The talk will be accessible to graduate students of any field of mathematics.
 
 
===Lillian Pierce (Duke University)===
 
  
Title: Short character sums
+
===Will Sawin (Columbia)===
  
Abstract: A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.
+
Title: On Chowla's Conjecture over F_q[T]
  
===Angelica Cueto (The Ohio State University)===
+
Abstract: The Mobius function in number theory is a sequences of 1s,
Title: Lines on cubic surfaces in the tropics
+
-1s, and 0s, which is simple to define and closely related to the
 +
prime numbers. Its behavior seems highly random. Chowla's conjecture
 +
is one precise formalization of this randomness, and has seen recent
 +
work by Matomaki, Radziwill, Tao, and Teravainen making progress on
 +
it. In joint work with Mark Shusterman, we modify this conjecture by
 +
replacing the natural numbers parameterizing this sequence with
 +
polynomials over a finite field. Under mild conditions on the finite
 +
field, we are able to prove a strong form of this conjecture. The
 +
proof is based on taking a geometric perspective on the problem, and
 +
succeeds because we are able to simplify the geometry using a trick
 +
based on the strange properties of polynomial derivatives over finite
 +
fields.
  
Abstract: Since the beginning of tropical geometry, a persistent challenge has been to emulate tropical versions of classical results in algebraic geometry. The well-know statement <i>any smooth surface of degree three in P^3 contains exactly 27 lines</i> is known to be false tropically. Work of Vigeland from 2007 provides examples of tropical cubic surfaces with infinitely many lines and gives a classification of tropical lines on general smooth tropical surfaces in TP^3.
 
  
In this talk I will explain how to correct this pathology by viewing the surface as a del Pezzo cubic and considering its embedding in P^44 via its anticanonical bundle. The combinatorics of the root system of type E_6 and a tropical notion of convexity will play a central role in the construction. This is joint work in progress with Anand Deopurkar.
+
===Yan Soibelman (Kansas State)===
  
===David Treumann (Boston College)===
+
Title: Riemann-Hilbert correspondence and Fukaya categories
  
Title: Twisting things in topology and symplectic topology by pth powers
+
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence
 +
for differential, q-difference and elliptic difference equations in dimension one.
 +
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation
 +
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles
 +
should appear as harmonic objects in this generalized non-abelian Hodge theory.
 +
All that is a part of the bigger project ``Holomorphic Floer theory",
 +
joint with Maxim Kontsevich.
  
Abstract: There's an old and popular analogy between circles and finite fields.  I'll describe some constructions you can make in Lagrangian Floer theory and in microlocal sheaf theory by taking this analogy extremely literally, the main ingredient is an "F-field."  An F-field on a manifold M is a local system of algebraically closed fields of characteristic p.  When M is symplectic, maybe an F-field should remind you of a B-field, it can be used to change the Fukaya category in about the same way.  On M = S^1 times R^3, this version of the Fukaya category is related to Deligne-Lusztig theory, and I found something like a cluster structure on the Deligne-Lusztig pairing varieties by studying it.  On M = S^1 times S^1, Yanki Lekili and I have found that this version of the Fukaya category is related to the equal-characteristic version of the Fargues-Fontaine curve; the relationship is homological mirror symmetry.
 
  
===Dean Baskin (Texas A&M)===
+
===Alicia Dickenstein (Buenos Aires)===
  
Title: Radiation fields for wave equations
+
Title: Algebra and geometry in the study of enzymatic cascades
  
Abstract: Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.
+
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.
 +
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.
  
===Jianfeng Lu (Duke University)===
 
  
Title: Density fitting: Analysis, algorithm and applications
+
=== Jianfeng Lu (Duke) ===
 +
Title: How to ``localize" the computation?
  
Abstract: Density fitting considers the low-rank approximation of pair products of eigenfunctions of Hamiltonian operators. It is a very useful tool with many applications in electronic structure theory. In this talk, we will discuss estimates of upper bound of the numerical rank of the pair products of eigenfunctions. We will also introduce the interpolative separable density fitting (ISDF) algorithm, which reduces the computational scaling of the low-rank approximation and can be used for efficient algorithms for electronic structure calculations. Based on joint works with Chris Sogge, Stefan Steinerberger, Kyle Thicke, and Lexing Ying.
+
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.
  
===Alexei Poltoratski (Texas A&M)===
+
===Eugenia Cheng (School of the Art Institute of Chicago)===
  
Title: Completeness of exponentials: Beurling-Malliavin and type problems
+
Title: Character vs gender in mathematics and beyond
  
Abstract: This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both
+
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.
problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin
 
problem was solved in the early 1960s and I will present its classical solution along with modern generalizations
 
and applications. I will then discuss history and recent progress in the type problem, which stood open for
 
more than 70 years.
 
  
===Li-Cheng Tsai (Columbia University)===
+
===Omer Mermelstein (Madison)===
  
Title: When particle systems meet PDEs
+
Title: Generic flat pregeometries
 +
 +
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.
 +
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.
  
Interacting particle systems are models that involve many randomly evolving agents (i.e., particles). These systems are widely used in describing real-world phenomena. In this talk we will walk through three facets of interacting particle systems, namely the law of large numbers, random fluctuations, and large deviations. Within each facet, I will explain how Partial Differential Equations (PDEs) play a role in understanding the systems.
 
  
===Aaron Naber (Northwestern)===
+
===Shamgar Gurevich (Madison)===
  
Title: A structure theory for spaces with lower Ricci curvature bounds.
+
Title: Harmonic Analysis on GL(n) over Finite Fields.
  
Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be?  This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like.  In this talk we give an essentially sharp answer to this question.  The talk will require little background, and our time will be spent on understanding the basic statements and examples.  The work discussed is joint with Cheeger, Jiang and with Li.
+
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:
  
 
+
trace(ρ(g)) / dim(ρ),
===Vladimir Sverak (Minnesota)===
+
 
+
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.
Title: PDE aspects of the Navier-Stokes equations and simpler models
+
   
 
+
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.  
Abstract: Does the Navier-Stokes equation give a reasonably complete description of fluid motion? There seems to be no empirical evidence which would suggest a negative answer (in regimes which are not extreme), but from the purely mathematical point of view, the answer may not be so clear. In the lecture, I will discuss some of the possible scenarios and open problems for both the full equations and simplified models.
+
   
 
+
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.
 
+
   
===Jason McCullough (Iowa State)===
+
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)
 
 
Title: On the degrees and complexity of algebraic varieties
 
 
 
Abstract: Given a system of polynomial equations in several variables, there are several natural questions regarding its associated solution set (algebraic variety): What is its dimension? Is it smooth or are there singularities?  How is it embedded in affine/projective space?  Free resolutions encode answers to all of these questions and are computable with modern computer algebra programs.  This begs the question: can one bound the computational complexity of a variety in terms of readily available data?  I will discuss two recently solved conjectures of Stillman and Eisenbud-Goto, how they relate to each other, and what they say about the complexity of algebraic varieties.
 
 
 
===Maksym Radziwill (Caltech)===
 
 
 
Title: Recent progress in multiplicative number theory
 
 
 
Abstract: Multiplicative number theory aims to understand the ways in which integers factorize, and the distribution of integers with special multiplicative properties (such as primes). It is a central area of analytic number theory with various connections to L-functions, harmonic analysis, combinatorics, probability etc. At the core of the subject lie difficult questions such as the Riemann Hypothesis, and they set a benchmark for its accomplishments.
 
An outstanding challenge in this field is to understand the multiplicative properties of integers linked by additive conditions, for instance n and n+ 1. A central conjecture making this precise is the Chowla-Elliott conjecture on correlations of multiplicative functions evaluated at consecutive integers. Until recently this conjecture appeared completely out of reach and was thought to be at least as difficult as showing the existence of infinitely many twin primes. These are also the kind of questions that lie beyond the capability of the Riemann Hypothesis.  However recently the landscape of multiplicative number theory has been changing and we are no longer so certain about the limitations of our (new) tools. I will discuss the recent progress on these questions.
 
 
 
===Jennifer Park (OSU)===
 
 
 
Title: Rational points on varieties
 
 
 
Abstract: The question of finding rational solutions to systems of polynomial equations has been investigated at least since the days of Pythagoras, but it is still not completely resolved (and in fact, it has been proven that there will never be an algorithm that answers this question!) Nonetheless, we will discuss various techniques that could answer this question in certain cases, and we will outline some conjectures related to this problem as well.
 
 
 
===Ju-Lee Kim (MIT)===
 
 
 
Title: Types and counting automorphic forms
 
 
 
Abstract: We review the theory of types in representations of p-adic groups and discuss some applications for quantifying automorphic forms.
 
 
 
===Eviatar Procaccia===
 
 
 
Title:  Can one hear the shape of a random walk?
 
 
 
Abstract: We consider a Gibbs distribution over random walk paths on the square lattice, proportional to a random weight of the path’s boundary . We show that in the zero temperature limit, the paths condensate around an asymptotic shape. This limit shape is characterized as the minimizer of the functional, mapping open connected subsets of the plane to the sum of their principle eigenvalue and perimeter (with respect to the first passage percolation norm). A prime novel feature of this limit shape is that it is not in the class of Wulff shapes.
 
Joint work with Marek Biskup (UCLA)
 
 
 
===Jo Nelson (Rice)===
 
 
 
Title: Contact Invariants and Reeb Dynamics
 
 
 
Abstract: Contact geometry is the study of certain geometric structures on odd dimensional smooth manifolds.  A contactstructure is a hyperplane field specified by a one form which satisfies a maximum nondegeneracy condition called complete non-integrability. The associated one form is called a contact form and uniquely determines a vector field called the Reeb vector field on the manifold. I will explain how to make use of J-holomorphic curves to obtain a Floer theoretic contact invariant, contact homology, whose chain complex is generated by closed Reeb orbits. In particular, I will explain the pitfalls in defining contact homology and discuss my work, in part joint with Hutchings, which provides rigorous constructions and applications to dynamics via geometric methods. This talk will feature numerous graphics to acclimate people to the realm of contact geometry.
 
 
 
===Justin Hsu (Madison)===
 
 
 
Title: From Couplings to Probabilistic Relational Program Logics
 
 
 
Abstract: Many program properties are relational, comparing the behavior of a program (or even two different programs) on two different inputs. While researchers have developed various techniques for verifying such properties for standard, deterministic programs, relational properties for probabilistic programs have been more challenging. In this talk, I will survey recent developments targeting a range of probabilistic relational properties, with motivations from privacy, cryptography, and machine learning. The key idea is to meld relational program logics with an idea from probability theory, called probabilistic couplings. The logics allow a highly compositional and surprisingly general style of program analysis, supporting clean proofs for a broad array of probabilistic relational properties.
 
 
 
=== Kavita Ramanan (Brown) ===
 
Title: Tales of Random Projections
 
 
 
Abstract: The interplay between geometry and probability in high-dimensional spaces is a subject of active research. Classical theorems in probability theory such as the central limit theorem and Cramer’s theorem can be viewed as providing information about certain scalar projections of high-dimensional product measures.  In this talk we will describe the behavior of random projections of more general (possibly non-product) high-dimensional measures, which are of interest in diverse fields, ranging from asymptotic convex geometry to high-dimensional statistics.  Although the study of (typical) projections of high-dimensional measures dates back to Borel, only recently has a theory begun to emerge, which in particular identifies the role of certain geometric assumptions that lead to better behaved projections.  A particular question of interest is to identify what properties of the high-dimensional measure are captured by  its lower-dimensional projections.  While fluctuations of these projections have been studied over the past decade, we describe more recent work on the tail behavior of multidimensional projections, and associated conditional limit theorems.
 
  
 
== Past Colloquia ==
 
== Past Colloquia ==
  
 
[[Colloquia/Blank|Blank]]
 
[[Colloquia/Blank|Blank]]
 +
 +
[[Colloquia/Spring2019|Spring 2019]]
  
 
[[Colloquia/Fall2018|Fall 2018]]
 
[[Colloquia/Fall2018|Fall 2018]]

Latest revision as of 19:57, 17 September 2019

Mathematics Colloquium

All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.


Fall 2019

date speaker title host(s)
Sept 6 Room 911 Will Sawin (Columbia) On Chowla's Conjecture over F_q[T] Marshall
Sept 13 Yan Soibelman (Kansas State) Riemann-Hilbert correspondence and Fukaya categories Caldararu
Sept 16 Monday Room 911 Alicia Dickenstein (Buenos Aires) Algebra and geometry in the study of enzymatic cascades Craciun
Sept 20 Jianfeng Lu (Duke) How to "localize" the computation? Qin
Sept 26 Thursday 3-4 pm Room 911 Eugenia Cheng (School of the Art Institute of Chicago) Character vs gender in mathematics and beyond Marshall / Friends of UW Madison Libraries
Sept 27 Omer Mermelstein (Madison) Generic flat pregeometries Andrews
Oct 4
Oct 11
Oct 18 Shamgar Gurevich (Madison) Harmonic Analysis on GL(n) over Finite Fields Marshall
Oct 25
Nov 1 Elchanan Mossel (MIT) Distinguished Lecture Roch
Nov 8 Reserved for job talk
Nov 15 Reserved for job talk
Nov 22 Reserved for job talk
Nov 29 Thanksgiving
Dec 6 Reserved for job talk
Dec 11 Wednesday Nick Higham (Manchester) LAA lecture Brualdi
Dec 13 Reserved for job talk

Spring 2020

date speaker title host(s)
Jan 24 Reserved for job talk
Jan 31 Reserved for job talk
Feb 7 Reserved for job talk
Feb 14 Reserved for job talk
Feb 21 Shai Evra (IAS) Gurevich
Feb 28 Brett Wick (Washington University, St. Louis) Seeger
March 6 Jessica Fintzen (Michigan) Marshall
March 13
March 20 Spring break
March 27 (Moduli Spaces Conference) Boggess, Sankar
April 3 Caroline Turnage-Butterbaugh (Carleton College) Marshall
April 10 Sarah Koch (Michigan) Bruce (WIMAW)
April 17 Song Sun (Berkeley) Huang
April 24 Natasa Sesum (Rutgers University) Angenent
May 1 Robert Lazarsfeld (Stony Brook) Distinguished lecture Erman

Abstracts

Will Sawin (Columbia)

Title: On Chowla's Conjecture over F_q[T]

Abstract: The Mobius function in number theory is a sequences of 1s, -1s, and 0s, which is simple to define and closely related to the prime numbers. Its behavior seems highly random. Chowla's conjecture is one precise formalization of this randomness, and has seen recent work by Matomaki, Radziwill, Tao, and Teravainen making progress on it. In joint work with Mark Shusterman, we modify this conjecture by replacing the natural numbers parameterizing this sequence with polynomials over a finite field. Under mild conditions on the finite field, we are able to prove a strong form of this conjecture. The proof is based on taking a geometric perspective on the problem, and succeeds because we are able to simplify the geometry using a trick based on the strange properties of polynomial derivatives over finite fields.


Yan Soibelman (Kansas State)

Title: Riemann-Hilbert correspondence and Fukaya categories

Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence for differential, q-difference and elliptic difference equations in dimension one. This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles should appear as harmonic objects in this generalized non-abelian Hodge theory. All that is a part of the bigger project ``Holomorphic Floer theory", joint with Maxim Kontsevich.


Alicia Dickenstein (Buenos Aires)

Title: Algebra and geometry in the study of enzymatic cascades

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. 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.


Jianfeng Lu (Duke)

Title: How to ``localize" the computation?

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.

Eugenia Cheng (School of the Art Institute of Chicago)

Title: Character vs gender in mathematics and beyond

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.

Omer Mermelstein (Madison)

Title: Generic flat pregeometries

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. 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.


Shamgar Gurevich (Madison)

Title: Harmonic Analysis on GL(n) over Finite Fields.

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:

trace(ρ(g)) / dim(ρ),

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.

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.

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.

This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)

Past Colloquia

Blank

Spring 2019

Fall 2018

Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012