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 ONLINE 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 2020=
+
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)
  
== September 25, 2020, [https://www.math.tamu.edu/~jml/  Joseph Landsberg] (Texas A&M) ==
+
'''Incidences and line counting: from the discrete to the fractal setting'''
  
(Hosted by Gurevitch)
+
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.
  
'''From theoretic computer science to algebraic geometry: how the complexity of matrix multiplication led me to the Hilbert scheme of points.'''
+
==September 30, 2022, Friday at 4pm [https://alejandraquintos.com/ Alejandra Quintos] (University of Wisconsin-Madison, Statistics) ==
 +
(host: Stovall)
  
In 1968 Strassen discovered the way we multiply nxn matrices
+
'''Dependent Stopping Times and an Application to Credit Risk Theory'''
(row/column)
 
is not the most efficient algorithm possible. Subsequent work has led to
 
the astounding conjecture that as the size n of the matrices grows, it
 
becomes
 
almost as easy to multiply matrices as it is to add them. I will give a
 
history
 
of this problem and explain why it is natural to study it using
 
algebraic geometry
 
and representation theory. I will conclude by discussing recent exciting
 
developments
 
that explain the second phrase in the title.
 
  
== October 9, 2020, [https://impa.br/en_US/page-pessoas/carolina-araujo/ Carolina Araujo] (IMPA) ==
+
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.
  
(Hosted by Ellenberg)
+
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 in Algebraic Geometry and Cremona transformations'''
+
==October 14, 2022, Friday at 4pm  [https://math.sciences.ncsu.edu/people/asagema/ Andrew Sageman-Furnas] (North Carolina State)==
 +
(host: Mari-Beffa)
  
In this talk I will discuss symmetries of complex algebraic varieties. When studying a projective variety $X$, one usually wants to understand its symmetries. Conversely, the structure of the group of automorphisms of $X$ encodes relevant geometric properties of $X$. After describing some examples of automorphism groups of projective varieties, I will discuss why the notion of automorphism is too rigid in the scope of birational geometry. We are then led to consider another class of symmetries of $X$, its birational self-maps. Birational self-maps of the projective space $\mathbb{P}^n$ are called Cremona transformations. Describing the structure of the group of Cremona transformations of the plane is a classical problem that goes back to the 19th century. In higher dimensions, not so much is known, and a natural problem is to construct interesting subgroups of the Cremona group. I will end by discussing a recent work with Alessio Corti and Alex Massarenti, where we investigate subgroups of the Cremona group consisting of symmetries preserving some special meromorphic volume forms.
+
== October 20, 2022, Thursday at 4pm, VV911  [https://tavarelab.cancerdynamics.columbia.edu/ Simon Tavaré] (Columbia University) ==
 +
(host: Kurtz, Roch)
  
== October 23, 2020, [http://www.math.toronto.edu/quastel/ Jeremy Quastel] (University of Toronto) ==
+
''Note the unusual time and room!''
  
(Hosted by Gorin)
+
'''An introduction to counts-of-counts data'''
  
'''Towards KPZ Universality'''
+
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
  
The 1-d KPZ universality class contains random interface growth models
+
''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.
as well as random polymer free energies and driven diffusive systems.
 
The KPZ fixed point has now been determined, through the exact solution of a special model
 
in the class, TASEP, and is expected to describe the asymptotic fluctuations for all models in the class.
 
It is an integrable Markov process, with transition probabilities described by a system of integrable PDE’s. 
 
Very recently, new techniques have become available to prove
 
the convergence of the KPZ equation itself, as well as some non-integrable extensions
 
of TASEP, to the KPZ fixed point.  This talk will be a gentle introduction to these developments
 
with no prior knowledge assumed.  The results are, variously, joint works with
 
Daniel Remenik, Konstantin Matetski, and Sourav Sarkar.
 
  
== November 6, 2020, [http://math.jhu.edu/~sakellar/ Yiannis Sakellaridis] (Johns Hopkins University)==
+
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.
  
(Hosted by Gurevitch)
+
''References''
  
'''Harmonic analysis, intersection cohomology, and L-functions.'''
+
[1] Fisher RA, Corbet AS & Williams CB. J Animal Ecology, 12, 1943
  
The goal of this lecture will be to describe a link between geometric-topological objects (certain intersection complexes on singular loop spaces), and objects of arithmetic interest (L-functions). The link between the two is by a Fourier/spectral transform. I will begin by giving an overview of Iwasawa–Tate theory, which expresses the Riemann zeta function as the Mellin transform of a certain theta series, and will conclude by describing joint work with Jonathan Wang (MIT), which expresses other L-functions as spectral transforms of functions obtained from intersection complexes on singular arc spaces. No prior familiarity with notions such as L-functions or intersection cohomology will be assumed.
+
[2] Arratia R, Barbour AD & Tavaré S. ''Logarithmic Combinatorial Structures,'' EMS, 2002
  
== November 20, 2020, [https://web.ma.utexas.edu/users/ntran/ Ngoc Mai Tran] (University of Texas) ==
+
[3] Ewens WJ. Theoret Popul Biol, 3, 1972
  
(Hosted by Rodriguez)
+
[4] Da Silva P, Jamshidpey A, McCullagh P & Tavaré S. Bernoulli Journal, in press, 2022 (online)
  
'''Does your problem have a tropical solution?'''
+
==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
  
Tropical mathematics is mathematics done in the min-plus (or max-plus) algebra.
+
(host: Yang).
The power of tropical mathematics comes from two key ideas: (a) tropical objects are limits of classical ones, and (b) the geometry of tropical objects is polyhedral. In this talk I'll demonstrate how these two ideas are used to solve a variety of problems in different domains the last 10 years, from deep neural networks, semigroups theory, auction theory and extreme value statistics.
 
  
== December 4, 2020, [http://math.sfsu.edu/federico/ Federico Ardila] (San Francisco) ==
+
== 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.
  
(Hosted by Ellenberg)
+
(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 ==
  
'''Measuring polytopes through their algebraic structure.'''
+
[[Colloquia/Fall2022|Fall 2022]]
  
Generalized permutahedra are a beautiful family of polytopes with a rich combinatorial structure, and strong connections to optimization and algebraic geometry. We prove they are the universal family of polyhedra with a certain Hopf-algebraic structure. This Hopf-algebraic structure is compatible with McMullen’s foundational work on the polytope algebra.
+
[[Colloquia/Spring2023|Spring 2023]]
  
Our construction provides a unifying framework to organize and study many combinatorial families; for example:
+
== Past Colloquia ==
 
+
[[Spring 2022 Colloquiums|Spring 2022]]
1. It uniformly answers open questions and recovers known results about graphs, posets, matroids, hypergraphs, simplicial complexes, and others.
 
 
 
2. It shows that permutahedra and associahedra “know" how to compute the multiplicative and compositional inverses of power series.
 
  
3. It explains the mysterious fact that many combinatorial invariants of matroids, posets, and graphs can also be thought of as measures on polytopes, satisfying the inclusion-exclusion relations.
+
[[Colloquia/Fall2021|Fall 2021]]
  
This is joint work with Marcelo Aguiar (2017) and Mario Sanchez (2020).
+
[[Colloquia/Spring2021|Spring 2021]]
  
== Past Colloquia ==
+
[[Colloquia/Fall2020|Fall 2020]]
  
 
[[Colloquia/Spring2020|Spring 2020]]
 
[[Colloquia/Spring2020|Spring 2020]]

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