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 20, 2022, Thursday at 4pm, VV911  [https://tavarelab.cancerdynamics.columbia.edu/ Simon Tavaré] (Columbia University) ==
 +
(host: Kurtz, Roch)
  
== 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) ==
+
''Note the unusual time and room!''
  
(reserved by the hiring committee)
+
'''An introduction to counts-of-counts data'''
  
'''Laplacian quadratic forms, function regularity, graphs, and optimal transport'''
+
Counts-of-counts data arise in many areas of biology and medicine, and have been studied by statisticians since the 1940s. One of the first examples, discussed by R. A. Fisher and collaborators in 1943 [1], concerns estimation of the number of unobserved species based on summary counts of the number of species observed once, twice, … in a sample of specimens. The data are summarized by the numbers ''C<sub>1</sub>, C<sub>2</sub>, '' of species represented once, twice, … in a sample of size
  
In this talk, I will discuss two different applications of harmonic analysis to
+
''N = C<sub>1</sub> + 2 C<sub>2</sub> + 3 C<sub>3</sub> + <sup>….</sup>''  containing ''S = C<sub>1</sub> + C<sub>2</sub> + <sup>…</sup>'' species; the vector ''C ='' ''(C<sub>1</sub>, C<sub>2</sub>, )'' gives the counts-of-counts. Other examples include the frequencies of the distinct alleles in a human genetics sample, the counts of distinct variants of the SARS-CoV-2 S protein obtained from consensus sequencing experiments, counts of sizes of components in certain combinatorial structures [2], and counts of the numbers of SNVs arising in one cell, two cells, … in a cancer sequencing experiment.
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) ==
+
In this talk I will outline some of the stochastic models used to model the distribution of ''C,'' and some of the inferential issues that come from estimating the parameters of these models. I will touch on the celebrated Ewens Sampling Formula [3] and Fisher’s multiple sampling problem concerning the variance expected between values of ''S'' in samples taken from the same population [3]. Variants of birth-death-immigration processes can be used, for example when different variants grow at different rates. Some of these models are mechanistic in spirit, others more statistical. For example, a non-mechanistic model is useful for describing the arrival of covid sequences at a database. Sequences arrive one at a time, and are either a new variant, or a copy of a variant that has appeared before. The classical Yule process with immigration provides a starting point to model this process, as I will illustrate.
  
(reserved by the hiring committee)
+
''References''
  
'''From simple groups to symmetries of surfaces'''
+
[1] Fisher RA, Corbet AS & Williams CB. J Animal Ecology, 12, 1943
  
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.
+
[2] Arratia R, Barbour AD & Tavaré S. ''Logarithmic Combinatorial Structures,'' EMS, 2002
  
== February 11, 2022, [https://people.math.wisc.edu/~msoskova/ Mariya Soskova] (UW-Madison) ==
+
[3] Ewens WJ. Theoret Popul Biol, 3, 1972
  
(local)
+
[4] Da Silva P, Jamshidpey A, McCullagh P & Tavaré S. Bernoulli Journal, in press, 2022 (online)
  
== February 18, 2022, [https://people.math.wisc.edu/~seeger/ Andreas Seeger] (UW-Madison) ==
+
==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
  
"Spherical maximal functions and fractal dimensions of dilation sets"
+
(host: Yang).
  
We survey old and new problems and results on spherical means, regarding pointwise convergence, $L^p$ improving and consequences for sparse domination.
+
== 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.
== February 25, 2022, [https://sites.google.com/view/rohini-ramadas/home Rohini Ramadas] (Warwick) ==
 
 
 
(hosted by WIMAW)
 
 
 
== March 2 and 4, 2022 (Wednesday and Friday),  [http://www.math.stonybrook.edu/~roblaz/ Robert Lazarsfeld] (Stony Brook) ==
 
 
 
('''Departmental Distinguished Lecture series''')
 
 
 
== March 11, 2022, [https://people.math.wisc.edu/~anderson/ David Anderson] (UW-Madison) ==
 
 
 
(local)
 
 
 
== March 25, 2022, [http://www.math.lsa.umich.edu/~canary/ Richard Canary] (Michigan) ==
 
 
 
(hosted by Zimmer)
 
 
 
== April 1, 2022, [https://www.patelp.com/ Priyam Patel] (Utah) ==
 
 
 
(hosted by WIMAW)
 
 
 
== April 8, 2022, [https://math.temple.edu/~tuf27009/index.html Matthew Stover] (Temple University) ==
 
 
 
(hosted by Zimmer)
 
 
 
== April 15, 2022, [https://www.qatar.tamu.edu/programs/science/faculty-and-staff/berhand-lamel Bernhard Lamel], (Texas A&M University at Qatar) ==
 
 
 
(hosted by Gong)
 
 
 
== April 22, 2022, [https://www.math.uni-kiel.de/analysis/de/mueller Detlef Müller] (Kiel, Germany) ==
 
 
 
(hosted by Seeger and Stovall)
 
 
 
== 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''')
 
  
 +
(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 102: Line 77:
  
 
== Past Colloquia ==
 
== Past Colloquia ==
 +
[[Spring 2022 Colloquiums|Spring 2022]]
 +
 
[[Colloquia/Fall2021|Fall 2021]]
 
[[Colloquia/Fall2021|Fall 2021]]
  

Latest revision as of 14:14, 30 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 20, 2022, Thursday at 4pm, VV911 Simon Tavaré (Columbia University)

(host: Kurtz, Roch)

Note the unusual time and room!

An introduction to counts-of-counts data

Counts-of-counts data arise in many areas of biology and medicine, and have been studied by statisticians since the 1940s. One of the first examples, discussed by R. A. Fisher and collaborators in 1943 [1], concerns estimation of the number of unobserved species based on summary counts of the number of species observed once, twice, … in a sample of specimens. The data are summarized by the numbers C1, C2, … of species represented once, twice, … in a sample of size

N = C1 + 2 C2 + 3 C3 + ….  containing S = C1 + C2 + species; the vector C = (C1, C2, …) gives the counts-of-counts. Other examples include the frequencies of the distinct alleles in a human genetics sample, the counts of distinct variants of the SARS-CoV-2 S protein obtained from consensus sequencing experiments, counts of sizes of components in certain combinatorial structures [2], and counts of the numbers of SNVs arising in one cell, two cells, … in a cancer sequencing experiment.

In this talk I will outline some of the stochastic models used to model the distribution of C, and some of the inferential issues that come from estimating the parameters of these models. I will touch on the celebrated Ewens Sampling Formula [3] and Fisher’s multiple sampling problem concerning the variance expected between values of S in samples taken from the same population [3]. Variants of birth-death-immigration processes can be used, for example when different variants grow at different rates. Some of these models are mechanistic in spirit, others more statistical. For example, a non-mechanistic model is useful for describing the arrival of covid sequences at a database. Sequences arrive one at a time, and are either a new variant, or a copy of a variant that has appeared before. The classical Yule process with immigration provides a starting point to model this process, as I will illustrate.

References

[1] Fisher RA, Corbet AS & Williams CB. J Animal Ecology, 12, 1943

[2] Arratia R, Barbour AD & Tavaré S. Logarithmic Combinatorial Structures, EMS, 2002

[3] Ewens WJ. Theoret Popul Biol, 3, 1972

[4] Da Silva P, Jamshidpey A, McCullagh P & Tavaré S. Bernoulli Journal, in press, 2022 (online)

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