Difference between revisions of "Colloquia"

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__NOTOC__
 
__NOTOC__
  
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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'''
  
=Fall 2021=
+
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)
  
== Sep. 17, 2021, B239, [https://markshus.wixsite.com/math Mark Shusterman] (Harvard) ==
+
'''Incidences and line counting: from the discrete to the fractal setting'''
  
(hosted by Gurevich)
+
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.
  
'''Finitely Presented Groups in Arithmetic Geometry'''
+
==September 30, 2022, Friday at 4pm [https://alejandraquintos.com/ Alejandra Quintos] (University of Wisconsin-Madison, Statistics) ==
 +
(host: Stovall)
  
I will report on recent works, in part joint with Esnault—Srinivas, and with Jarden, on the finite presentability of several (profinite) groups arising in algebraic geometry and in number theory. These results build on a cohomological criterion of Lubotzky involving Euler characteristics. I will try to explain the analogy, rooted in arithmetic topology, between these results and classical facts about fundamental groups of three-dimensional manifolds.
+
'''Dependent Stopping Times and an Application to Credit Risk Theory'''
  
== Sep. 24, 2021 , [https://math.wisc.edu/staff/paul-sean/ Sean Paul] (UW-Madison) ==
+
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  [https://www.daniellitt.com/ Daniel Litt] (University of Toronto)==
 +
(host: Ananth Shankar)
  
 +
'''The search for special symmetries'''
  
== October 8, 2021 , [https://www.maths.ox.ac.uk/people/jon.chapman Jon Chapman] (University of Oxford) ==
+
What are the canonical sets of symmetries of n-dimensional space? I'll describe the history of this question, going back to Schwarz, Fuchs, Painlevé, and others, and some new answers to it, obtained jointly with Aaron Landesman. While our results rely on low-dimensional topology, Hodge theory, and the Langlands program, and we'll get a peek into how these areas come into play, no knowledge of them will be assumed.
  
(Wasow lecture; hosted by Thiffeault)
+
==October 14, 2022, Friday at 4pm  [https://math.sciences.ncsu.edu/people/asagema/ Andrew Sageman-Furnas] (North Carolina State)==
 +
(host: Mari-Beffa)
  
== October 11, 13, 15, 2021 '''[Mon, Wed, Fri 4-5pm]''', [https://www.maths.usyd.edu.au/u/geordie/ Geordie Williamson] (University of Sydney) ==
+
'''Constructing isometric tori with the same curvatures'''
  
(Special lecture series; hosted by Gurevich)
+
Which data determine an immersed surface in Euclidean three-space up to rigid motion? A generic surface is locally determined by only an intrinsic metric and extrinsic mean curvature function. However, there are exceptions. These may arise in a family like the isometric family of vanishing mean curvature surfaces transforming a catenoid into a helicoid.
  
== October 29, 2021 , [https://web.math.princeton.edu/~aionescu/ Alexandru Ionescu] (Princeton University) ==
+
For compact surfaces, Lawson and Tribuzy proved in 1981 that a metric and non-constant mean curvature function determine at most one immersion with genus zero, but at most two compact immersions (compact Bonnet pairs) for higher genus. In this talk, we discuss our recent construction of the first examples of compact Bonnet pairs. It uses a local classification by Kamberov, Pedit, and Pinkall in terms of isothermic surfaces. Moreover, we describe how a structure-preserving discrete theory for isothermic surfaces and Bonnet pairs led to this discovery.
  
(hosted by Wainger)
+
The smooth theory is joint work with Alexander Bobenko and Tim Hoffmann and the discrete theory is joint work with Tim Hoffmann and Max Wardetzky.
  
== November 5, 2021 , [https://faculty.washington.edu/jathreya/ Jayadev S. Athreya] (University of Washington) ==
+
== October 20, 2022, Thursday at 4pm, VV911  [https://tavarelab.cancerdynamics.columbia.edu/ Simon Tavaré] (Columbia University) ==
 +
(host: Kurtz, Roch)
  
(hosted by Uyanik)
+
''Note the unusual time and room!''
  
== November 12, 2021 , [https://sites.tufts.edu/kasso/ Kasso Okoudjou] (Tufts University) ==
+
'''An introduction to counts-of-counts data'''
  
(hosted by Stovall)
+
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
  
== Nov. 19, 2021 , [https://math.wisc.edu/ TBA] (TBA) ==
+
''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.
  
(reserved by the hiring committee)
+
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.
  
== Dec. 3, 2021 , [https://math.wisc.edu/ TBA] (TBA) ==
+
''References''
  
(reserved by the hiring committee)
+
[1] Fisher RA, Corbet AS & Williams CB. J Animal Ecology, 12, 1943
  
== Dec. 10, 2021 , [https://math.wisc.edu/ TBA] (TBA) ==
+
[2] Arratia R, Barbour AD & Tavaré S. ''Logarithmic Combinatorial Structures,'' EMS, 2002
  
(reserved by the hiring committee)
+
[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  [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
  
== Future ==
+
(host: Yang).
  
[[Colloquia/Spring2022|Spring 2022]]
+
== 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.
 +
 
 +
(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 ==
 +
 
 +
[[Colloquia/Fall2022|Fall 2022]]
 +
 
 +
[[Colloquia/Spring2023|Spring 2023]]
  
 
== Past Colloquia ==
 
== Past Colloquia ==
 +
[[Spring 2022 Colloquiums|Spring 2022]]
 +
 +
[[Colloquia/Fall2021|Fall 2021]]
  
 
[[Colloquia/Spring2021|Spring 2021]]
 
[[Colloquia/Spring2021|Spring 2021]]

Latest revision as of 10:04, 3 October 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)

The search for special symmetries

What are the canonical sets of symmetries of n-dimensional space? I'll describe the history of this question, going back to Schwarz, Fuchs, Painlevé, and others, and some new answers to it, obtained jointly with Aaron Landesman. While our results rely on low-dimensional topology, Hodge theory, and the Langlands program, and we'll get a peek into how these areas come into play, no knowledge of them will be assumed.

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

(host: Mari-Beffa)

Constructing isometric tori with the same curvatures

Which data determine an immersed surface in Euclidean three-space up to rigid motion? A generic surface is locally determined by only an intrinsic metric and extrinsic mean curvature function. However, there are exceptions. These may arise in a family like the isometric family of vanishing mean curvature surfaces transforming a catenoid into a helicoid.

For compact surfaces, Lawson and Tribuzy proved in 1981 that a metric and non-constant mean curvature function determine at most one immersion with genus zero, but at most two compact immersions (compact Bonnet pairs) for higher genus. In this talk, we discuss our recent construction of the first examples of compact Bonnet pairs. It uses a local classification by Kamberov, Pedit, and Pinkall in terms of isothermic surfaces. Moreover, we describe how a structure-preserving discrete theory for isothermic surfaces and Bonnet pairs led to this discovery.

The smooth theory is joint work with Alexander Bobenko and Tim Hoffmann and the discrete theory is joint work with Tim Hoffmann and Max Wardetzky.

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