Difference between revisions of "Colloquia"

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__NOTOC__
 
__NOTOC__
  
 +
In 2022-2023, our colloquia will be in-person talks in B239 unless otherwise stated.
  
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b>
+
==September 9 , 2022, Friday at 4pm  [https://math.ou.edu/~jing/ Jing Tao] (University of Oklahoma)==
 +
(host: Dymarz, Uyanik, WIMAW)
  
<!--- in Van Vleck B239, '''unless otherwise indicated'''. --->
+
'''On surface homeomorphisms'''
  
 +
In the 1970s, Thurston generalized the classification of self-maps of the torus to surfaces of higher genus, thus completing the work initiated by Nielsen. This is known as the Nielsen-Thurston Classification Theorem. Over the years, many alternative proofs have been obtained, using different aspects of surface theory. In this talk, I will overview the classical theory and sketch the ideas of a new proof, one that offers new insights into the hyperbolic geometry of surfaces. This is joint work with Camille Horbez.
 +
==September 23, 2022, Friday at 4pm  [https://www.pabloshmerkin.org/ Pablo Shmerkin] (University of British Columbia) ==
 +
(host: Guo, Seeger)
  
== January 10, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://www.stat.berkeley.edu/~gheissari/ Reza Gheissari] (UC Berkeley) ==
+
'''Incidences and line counting: from the discrete to the fractal setting'''
  
(reserved by the hiring committee)
+
How many lines are spanned by a set of planar points?. If the points are collinear, then the answer is clearly "one". If they are not collinear, however, several different answers exist when sets are finite and "how many" is measured by cardinality. I will discuss a bit of the history of this problem and present a recent extension to the continuum setting, obtained in collaboration with T. Orponen and H. Wang. No specialized background will be assumed.
  
'''Surface phenomena in the 2D and 3D Ising model'''
+
==September 30, 2022, Friday at 4pm [https://alejandraquintos.com/ Alejandra Quintos] (University of Wisconsin-Madison, Statistics) ==
 +
(host: Stovall)
  
Since its introduction in 1920, the Ising model has been one of the most studied models of phase transitions in statistical physics. In its low-temperature regime, the model has two thermodynamically stable phases, which, when in contact with each other, form an interface: a random curve in 2D and a random surface in 3D. In this talk, I will survey the rich phenomenology of this interface in 2D and 3D, and describe recent progress in understanding its geometry in various parameter regimes where different surface phenomena and universality classes emerge.
+
'''Dependent Stopping Times and an Application to Credit Risk Theory'''
  
== January 17, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/lovingmath/home Marissa Loving] (Georgia Tech) ==
+
Stopping times are used in applications to model random arrivals. A standard assumption in many models is that the stopping times are conditionally independent, given an underlying filtration. This is a widely useful assumption, but there are circumstances where it seems to be unnecessarily strong. In the first part of the talk, we use a modified Cox construction, along with the bivariate exponential introduced by Marshall & Olkin (1967), to create a family of stopping times, which are not necessarily conditionally independent, allowing for a positive probability for them to be equal. We also present a series of results exploring the special properties of this construction.
  
(reserved by the hiring committee)
+
In the second part of the talk, we present an application of our model to Credit Risk. We characterize the probability of a market failure which is defined as the default of two or more globally systemically important banks (G-SIBs) in a small interval of time. The default probabilities of the G-SIBs are correlated through the possible existence of a market-wide stress event. We derive various theorems related to market failure probabilities, such as the probability of a catastrophic market failure, the impact of increasing the number of G-SIBs in an economy, and the impact of changing the initial conditions of the economy's state variables. We also show that if there are too many G-SIBs, a market failure is inevitable, i.e., the probability of a market failure tends to one as the number of G-SIBs tends to infinity.
 +
==October 7, 2022, Friday at 4pm  [https://www.daniellitt.com/ Daniel Litt] (University of Toronto)==
 +
(host: Ananth Shankar)
  
'''Symmetries of surfaces: big and small'''
+
==October 14, 2022, Friday at 4pm  [https://math.sciences.ncsu.edu/people/asagema/ Andrew Sageman-Furnas] (North Carolina State)==
 +
(host: Mari-Beffa)
  
We will introduce both finite and infinite-type surfaces and study their collections of symmetries, known as mapping class groups. The study of the mapping class group of finite-type surfaces has played a central role in low-dimensional topology stretching back a hundred years to work of Max Dehn and Jakob Nielsen, and gaining momentum and significance through the celebrated work of Bill Thurston on the geometry of 3-manifolds. In comparison, the study of the mapping class group of infinite-type surfaces has exploded only within the past few years. Nevertheless, infinite-type surfaces appear quite regularly in the wilds of mathematics with connections to dynamics, the topology of 3-manifolds, and even descriptive set theory -- there is a great deal of rich mathematics to be gained in their study! In this talk, we will discuss the way that the study of surfaces intersects and interacts with geometry, algebra, and number theory, as well as some of my own contributions to this vibrant area of study.
+
==October 21, 2022, Friday at 4pm  [https://web.ma.utexas.edu/users/ntran/ Ngoc Mai Tran] (Texas)==
 +
(host: Rodriguez)
 +
== November 7-9, 2022, [https://ai.facebook.com/people/kristin-lauter/ Kristen Lauter] (Facebook) ==
 +
Distinguished lectures
  
== January 21, 2022, Friday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://web.math.princeton.edu/~nfm2/ Nicholas Marshall]  (Princeton) ==
+
(host: Yang).
  
(reserved by the hiring committee)
+
== November 11, 2022, Friday at 4pm [http://users.cms.caltech.edu/~jtropp/ Joel Tropp] (Caltech)==
 
+
This is the Annual LAA lecture. See [https://math.wisc.edu/laa-lecture/ this] for its history.
'''Laplacian quadratic forms, function regularity, graphs, and optimal transport'''
 
 
 
In this talk, I will discuss two different applications of harmonic analysis to
 
problems motivated by data science. Both problems involve using Laplacian
 
quadratic forms to measure the regularity of functions. In both cases the key
 
idea is to understand how to modify these quadratic forms to achieve a specific
 
goal. First, in the graph setting, we suppose that a collection of m graphs
 
G_1 = (V,E_1),...,G_m=(V,E_m) on a common set of vertices V is given,
 
and consider the problem of finding the 'smoothest' function f : V -> R with
 
respect to all graphs simultaneously, where the notion of smoothness is defined
 
using graph Laplacian quadratic forms. Second, on the unit square [0,1]^2, we
 
consider the problem of efficiently computing linearizations of 2-Wasserstein
 
distance; here, the solution involves quadratic forms of a Witten Laplacian.
 
 
 
== January 24, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/skippermath Rachel Skipper] (Ohio State) ==
 
 
 
(reserved by the hiring committee)
 
 
 
'''From simple groups to symmetries of surfaces'''
 
 
 
We will take a tour through some families of groups of historic importance in geometric group theory, including self-similar groups and Thompson’s groups. We will discuss the rich, continually developing theory of these groups which act as symmetries of the Cantor space, and how they can be used to understand the variety of infinite simple groups. Finally, we will discuss how these groups are serving an important role in the newly developing field of big mapping class groups which are used to describe symmetries of surfaces.
 
 
 
== February 11, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://people.math.wisc.edu/~msoskova/ Mariya Soskova] (UW-Madison) ==
 
 
 
'''The e-verse'''
 
 
 
Computability theory studies the relative algorithmic complexity of sets of natural numbers and other mathematical objects. Turing reducibility and the induced partial order of the Turing degrees serve as the well-established model of relative computability. Enumeration reducibility captures another natural relationship between sets of natural numbers in which positive information about the first set is used to produce positive information about the second set. The induced structure of the enumeration degrees can be viewed as an extension of the Turing degrees, as there is a natural way to embed the second partial order in the first. In certain cases, the enumeration degrees can be used to capture the algorithmic content of mathematical objects, while the Turing degrees fail. Certain open problems in degree theory present as more approachable in the extended context of the enumeration degrees, e.g. first order definability. We have been working to develop a richer “e-verse”: a system of classes of enumeration degrees with interesting properties and relationships, in order to better understand the enumeration degrees. I will outline several research directions in this context.
 
 
 
== February 18, 2022, at 4pm in B239 + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Video over Zoom], [https://people.math.wisc.edu/~seeger/ Andreas Seeger] (UW-Madison) ==
 
 
 
'''Spherical maximal functions and fractal dimensions of dilation sets'''
 
 
 
We survey old and new problems and results on spherical means, regarding pointwise convergence, $L^p$ improving and consequences for sparse domination.
 
 
 
== February 25, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live Stream], [https://sites.google.com/view/rohini-ramadas/home Rohini Ramadas] (Warwick) ==
 
 
 
(hosted by WIMAW)
 
 
 
'''Dynamics on the moduli space of point-configurations on the Riemann sphere'''
 
 
 
A degree-$d$ rational function $f(z)$ in one variable with complex coefficients defines a holomorphic self-map of the Riemann sphere. A rational function is called post-critically finite (PCF) if every critical point is (pre)-periodic. PCF rational functions have been central in complex dynamics, due to their special dynamical behavior, and their special distribution within the parameter space of all rational maps.
 
 
 
By work of Koch building on a result of Thurston, every PCF map arises as an isolated fixed point of an algebraic dynamical system on the moduli space $M_{0,n}$ of point-configurations on the Riemann sphere. I will introduce PCF maps and $M_{0,n}$. I will then present results characterizing the ensuing dynamics on $M_{0,n}$.
 
 
 
This talk includes joint work with Nguyen-Bac Dang, Sarah Koch, David Speyer, and Rob Silversmith.
 
 
 
== March 1, 2 and 4, 2022 (Tuesday, Wednesday and Friday),  [http://www.math.stonybrook.edu/~roblaz/ Robert Lazarsfeld] (Stony Brook) ==
 
(''Departmental Distinguished Lecture series'')
 
 
 
'''Public Lecture: Pythagorean triples and parametrized curves'''
 
 
 
''Tuesday, March 1, 4:00pm (Humanities 3650 + [http://go.wisc.edu/n6986j Live Stream]). Note unusual time and location!''
 
 
 
In this lecture, aimed at advanced undergraduate and beginning graduate students, I will discuss the question of when a curve in the plane admits a parameterization by polynomials or rational functions.
 
 
 
 
 
'''Colloquium: How irrational is an irrational variety?'''
 
 
 
''Wednesday, March 2, 4:00pm (VV B239 + [http://go.wisc.edu/wuas48 Live Stream]).''
 
 
 
Recall that an algebraic variety is said to be rational if it has a Zariski open subset that is isomorphic to an open subset of projective space. There has been a great deal of recent activity and progress on questions of rationality, but most varieties aren't rational. I will survey a body of work concerned with measuring and controlling “how irrational” a given variety might be.
 
 
 
 
 
'''Seminar: Measures of association for algebraic varieties'''
 
 
 
''Friday, March 4, 4:00pm (VV B239 )''
 
 
 
I will discuss some recent work with Olivier Martin that attempts to quantify how far two varieties are from being birationally isomorphic. Besides presenting a few results, I will discuss many open problems and avenues for further investigation.
 
 
 
== March 11, 2022, [https://people.math.wisc.edu/~anderson/ David Anderson] (UW-Madison) ==
 
 
 
'''Stochastic models of reaction networks and the Chemical Recurrence Conjecture'''
 
 
 
Cellular, chemical, and population processes are all often represented via networks that describe the interactions between the different population types (typically called the ''species'').   
 
 
 
If the counts of the species are low, then these systems are most often modeled as continuous-time Markov chains on $Z^d$ (with d being the number of species), with rates determined by stochastic mass-action kinetics.  A natural (broad) question is:  how do the qualitative properties of the dynamical system relate to the properties of the network?  One specific conjecture, called the Chemical Recurrence Conjecture, and that has been open for decades, is the following: if each connected component of the network is strongly connected, then the associated stochastic model is positive recurrent (meaning the model is quite stable). 
 
 
 
I will give a general introduction to this class of models and will present the latest work towards a proof of the Chemical Recurrence Conjecture.  I will make this talk accessible to graduate students, regardless of their field of study.  Some of the new results presented are joint with Daniele Cappelletti, Andrea Agazzi, and Jonathan Mattingly.
 
 
 
== March 25, 2022, Friday at 4pm on [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Zoom]. [http://www.math.lsa.umich.edu/~canary/ Richard Canary] (Michigan) ==
 
 
 
(hosted by Zimmer)
 
 
 
'''Hitchin representations of Fuchsian groups'''
 
 
 
Abstract:  The Teichm&uuml;ller space $\mathcal T(S)$ of all hyperbolic structures on a fixed closed surface $S$ is a central object in geometry, topology and dynamics. It may be viewed  as the orbifold universal cover of the moduli space of algebraic curves of fixed genus and also as a component of the space of (conjugacy classes of) representations of $\pi_1(S)$ into $\mathsf{PSL}(2,\mathbb R)$ which is topologically a cell.
 
Hitchin discovered a component $\mathcal H_d(S)$ of the space of (conjugacy classes of) representations of $\pi_1(S)$ into $\mathsf{PSL}(d,\mathbb R)$
 
which is topologically a cell. Subsequently, many striking analogies between the Hitchin component $\mathcal H_d(S)$ and Teichm&uuml;ller space $\mathcal T(S)$ were found. For example, Labourie showed that all representations in $\mathcal H_d(S)$ are discrete, faithful quasi-isometric embeddings.
 
 
 
In this talk, we will begin by gently reviewing the parallel theories of Teichm&uuml;ller space and the Hitchin component. We will finish by reviewing a long term project to develop a geometric theory of the augmented Hitchin component which parallels the classical theory of the augmented Hitchin component (which one may view as the "orbifold universal cover" of the Deligne-Mumford compactification of Teichm&uuml;ller space). This program includes joint work with Harry Bray, Nyima Kao, Giuseppe Martone, Tengren Zhang and Andy Zimmer.
 
 
 
== April 1, 2022, Friday at 4pm in B239 + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Zoom broadcast], [https://www.patelp.com/ Priyam Patel] (Utah) ==
 
 
 
(hosted by WIMAW)
 
 
 
'''Infinite-type surfaces'''
 
 
 
Surfaces fall into two categories: finite-type and infinite-type. The theory of infinite-type surfaces has been historically less developed than that of finite-type surfaces, but in the last few years, there has been a surge of interest in surfaces of infinite type and their mapping class groups (informally thought of as the groups of topological symmetries of these surfaces). In this talk, I will survey some of the biggest open problems in this quickly growing subfield of geometric group theory and topology, and discuss some of my own recent joint work towards resolving them.
 
 
 
== April 8, 2022, Friday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream], [https://math.temple.edu/~tuf27009/index.html Matthew Stover] (Temple University) ==
 
 
 
(hosted by Zimmer)
 
 
 
'''A geometric characterization of arithmeticity'''
 
 
 
An old, fundamental problem is classifying closed n-manifolds admitting a metric of constant curvature. The most mysterious case is constant curvature -1, that is, hyperbolic manifolds, and these divide further into "arithmetic" and "nonarithmetic" manifolds. However, it is not at all evident from the definitions that this distinction has anything to do with the differential geometry of the manifold. Uri Bader, David Fisher, Nicholas Miller and I gave a geometric characterization of arithmeticity in terms of properly immersed totally geodesic submanifolds, answering a question due independently to Alan Reid and Curtis McMullen. I will give an overview, assuming only basic differential topology, of how (non)arithmeticity and totally geodesic submanifolds are connected, then describe how this allows us to import tools from ergodic theory and homogeneous dynamics originating in groundbreaking work of Margulis to prove our characterization. Given time, I will mention some more recent developments and open questions.
 
 
 
== April 15, 2022, Friday at 4pm in B239, [https://www.qatar.tamu.edu/programs/science/faculty-and-staff/berhand-lamel Bernhard Lamel], (Texas A&M University at Qatar) ==
 
 
 
(hosted by Gong)
 
 
 
'''Convergence and Divergence of Formal Power Series Maps'''
 
 
 
Consider two real-analytic hypersurfaces (i.e. defined by convergent power series) in complex spaces. A formal holomorphic map is said to take one into the other if the composition of the power series defining the target with the map (which is just another formal power series) is a (formal) multiple of the defining power series of the source. In this talk, we are going to be interested in conditions for formal holomorphic maps to necessarily be convergent. Now, a formal holomorphic map taking the real line to itself is just a formal power series with real coefficients; this example also gives rise to real hypersurfaces in higher dimensional complex spaces having divergent formal self-maps. On the other hand, a formal map taking the unit sphere in higher dimensional complex space to itself is necessarily a rational map with poles outside of the sphere, in particular, the formal power series defining it converges. The convergence theory for formal self-maps of real hypersurfaces has been developed in the late 1990s and early 2000s. For formal embeddings, “ideal" conditions had been long conjectured. I’m going to give an introduction to this problem and talk about some joint work from 2018 with Nordine Mir giving a basically complete answer to the question when a formal map taking a real-analytic hypersurface in complex space into another one is necessarily convergent.
 
 
 
== April 25-26-27 (Monday [VV B239], Tuesday [Chamberlin 2241], Wednesday [VV B239]) 4 pm  [https://math.mit.edu/directory/profile.php?pid=1461 Larry Guth] (MIT) ==
 
 
 
(''Departmental Distinguished Lecture series'')
 
 
 
== May 10+12, 2022, Tuesday+Thursday, 12pm on Zoom. [http://www.ma.huji.ac.il/~kalai/ Gil Kalai] (Hebrew University) ==
 
 
 
(''Hilldale Lectures / Special colloquium'')
 
 
 
'''The argument against quantum computers'''
 
  
 +
(host: Qin, Jordan)
 +
==November 18, 2022, Friday at 4pm  [TBD]==
 +
(reserved by HC. contact: Stechmann)
 +
==December 2, 2022, Friday at 4pm  [TBD]==
 +
(reserved by HC. contact: Stechmann)
 +
==December 9, 2022, Friday at 4pm  [TBD]==
 +
(reserved by HC. contact: Stechmann)
 
== Future Colloquia ==
 
== Future Colloquia ==
  
Line 159: Line 54:
  
 
== Past Colloquia ==
 
== Past Colloquia ==
 +
[[Spring 2022 Colloquiums|Spring 2022]]
 +
 
[[Colloquia/Fall2021|Fall 2021]]
 
[[Colloquia/Fall2021|Fall 2021]]
  

Latest revision as of 06:38, 21 September 2022


In 2022-2023, our colloquia will be in-person talks in B239 unless otherwise stated.

September 9 , 2022, Friday at 4pm Jing Tao (University of Oklahoma)

(host: Dymarz, Uyanik, WIMAW)

On surface homeomorphisms

In the 1970s, Thurston generalized the classification of self-maps of the torus to surfaces of higher genus, thus completing the work initiated by Nielsen. This is known as the Nielsen-Thurston Classification Theorem. Over the years, many alternative proofs have been obtained, using different aspects of surface theory. In this talk, I will overview the classical theory and sketch the ideas of a new proof, one that offers new insights into the hyperbolic geometry of surfaces. This is joint work with Camille Horbez.

September 23, 2022, Friday at 4pm Pablo Shmerkin (University of British Columbia)

(host: Guo, Seeger)

Incidences and line counting: from the discrete to the fractal setting

How many lines are spanned by a set of planar points?. If the points are collinear, then the answer is clearly "one". If they are not collinear, however, several different answers exist when sets are finite and "how many" is measured by cardinality. I will discuss a bit of the history of this problem and present a recent extension to the continuum setting, obtained in collaboration with T. Orponen and H. Wang. No specialized background will be assumed.

September 30, 2022, Friday at 4pm Alejandra Quintos (University of Wisconsin-Madison, Statistics)

(host: Stovall)

Dependent Stopping Times and an Application to Credit Risk Theory

Stopping times are used in applications to model random arrivals. A standard assumption in many models is that the stopping times are conditionally independent, given an underlying filtration. This is a widely useful assumption, but there are circumstances where it seems to be unnecessarily strong. In the first part of the talk, we use a modified Cox construction, along with the bivariate exponential introduced by Marshall & Olkin (1967), to create a family of stopping times, which are not necessarily conditionally independent, allowing for a positive probability for them to be equal. We also present a series of results exploring the special properties of this construction.

In the second part of the talk, we present an application of our model to Credit Risk. We characterize the probability of a market failure which is defined as the default of two or more globally systemically important banks (G-SIBs) in a small interval of time. The default probabilities of the G-SIBs are correlated through the possible existence of a market-wide stress event. We derive various theorems related to market failure probabilities, such as the probability of a catastrophic market failure, the impact of increasing the number of G-SIBs in an economy, and the impact of changing the initial conditions of the economy's state variables. We also show that if there are too many G-SIBs, a market failure is inevitable, i.e., the probability of a market failure tends to one as the number of G-SIBs tends to infinity.

October 7, 2022, Friday at 4pm Daniel Litt (University of Toronto)

(host: Ananth Shankar)

October 14, 2022, Friday at 4pm Andrew Sageman-Furnas (North Carolina State)

(host: Mari-Beffa)

October 21, 2022, Friday at 4pm Ngoc Mai Tran (Texas)

(host: Rodriguez)

November 7-9, 2022, Kristen Lauter (Facebook)

Distinguished lectures

(host: Yang).

November 11, 2022, Friday at 4pm Joel Tropp (Caltech)

This is the Annual LAA lecture. See this for its history.

(host: Qin, Jordan)

November 18, 2022, Friday at 4pm [TBD]

(reserved by HC. contact: Stechmann)

December 2, 2022, Friday at 4pm [TBD]

(reserved by HC. contact: Stechmann)

December 9, 2022, Friday at 4pm [TBD]

(reserved by HC. contact: Stechmann)

Future Colloquia

Fall 2022

Spring 2023

Past Colloquia

Spring 2022

Fall 2021

Spring 2021

Fall 2020

Spring 2020

Fall 2019

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

WIMAW