https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Vadicgor&feedformat=atomUW-Math Wiki - User contributions [en]2020-09-19T23:08:14ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19887Colloquia2020-09-18T20:23:42Z<p>Vadicgor: /* December 4, 2020, Federico Ardila (San Francisco) */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2020=<br />
<br />
== September 25, 2020, [https://www.math.tamu.edu/~jml/ Joseph Landsberg] (Texas A&M) ==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
'''From theoretic computer science to algebraic geometry: how the complexity of matrix multiplication led me to the Hilbert scheme of points.'''<br />
<br />
In 1968 Strassen discovered the way we multiply nxn matrices<br />
(row/column)<br />
is not the most efficient algorithm possible. Subsequent work has led to<br />
the astounding conjecture that as the size n of the matrices grows, it<br />
becomes<br />
almost as easy to multiply matrices as it is to add them. I will give a<br />
history<br />
of this problem and explain why it is natural to study it using<br />
algebraic geometry<br />
and representation theory. I will conclude by discussing recent exciting<br />
developments<br />
that explain the second phrase in the title.<br />
<br />
== October 9, 2020, [https://impa.br/en_US/page-pessoas/carolina-araujo/ Carolina Araujo] (IMPA) ==<br />
<br />
(Hosted by Ellenberg)<br />
<br />
== October 23, 2020, [http://www.math.toronto.edu/quastel/ Jeremy Quastel] (University of Toronto) ==<br />
<br />
(Hosted by Gorin)<br />
<br />
== November 6, 2020, [http://math.jhu.edu/~sakellar/ Yiannis Sakellaridis] (Johns Hopkins University)==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
== November 20, 2020, TBA ==<br />
<br />
== December 4, 2020, [http://math.sfsu.edu/federico/ Federico Ardila] (San Francisco) ==<br />
<br />
(Hosted by Ellenberg)<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19886Colloquia2020-09-18T20:23:26Z<p>Vadicgor: /* December 4, 2020, TBA */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2020=<br />
<br />
== September 25, 2020, [https://www.math.tamu.edu/~jml/ Joseph Landsberg] (Texas A&M) ==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
'''From theoretic computer science to algebraic geometry: how the complexity of matrix multiplication led me to the Hilbert scheme of points.'''<br />
<br />
In 1968 Strassen discovered the way we multiply nxn matrices<br />
(row/column)<br />
is not the most efficient algorithm possible. Subsequent work has led to<br />
the astounding conjecture that as the size n of the matrices grows, it<br />
becomes<br />
almost as easy to multiply matrices as it is to add them. I will give a<br />
history<br />
of this problem and explain why it is natural to study it using<br />
algebraic geometry<br />
and representation theory. I will conclude by discussing recent exciting<br />
developments<br />
that explain the second phrase in the title.<br />
<br />
== October 9, 2020, [https://impa.br/en_US/page-pessoas/carolina-araujo/ Carolina Araujo] (IMPA) ==<br />
<br />
(Hosted by Ellenberg)<br />
<br />
== October 23, 2020, [http://www.math.toronto.edu/quastel/ Jeremy Quastel] (University of Toronto) ==<br />
<br />
(Hosted by Gorin)<br />
<br />
== November 6, 2020, [http://math.jhu.edu/~sakellar/ Yiannis Sakellaridis] (Johns Hopkins University)==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
== November 20, 2020, TBA ==<br />
<br />
== December 4, 2020, [http://math.sfsu.edu/federico/ Federico Ardila] (San Francisco) ==<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19870Colloquia2020-09-18T16:15:57Z<p>Vadicgor: /* September 25, 2020, Joseph Landsberg (Texas A&M) */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2020=<br />
<br />
== September 25, 2020, [https://www.math.tamu.edu/~jml/ Joseph Landsberg] (Texas A&M) ==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
'''From theoretic computer science to algebraic geometry: how the complexity of matrix multiplication led me to the Hilbert scheme of points.'''<br />
<br />
In 1968 Strassen discovered the way we multiply nxn matrices<br />
(row/column)<br />
is not the most efficient algorithm possible. Subsequent work has led to<br />
the astounding conjecture that as the size n of the matrices grows, it<br />
becomes<br />
almost as easy to multiply matrices as it is to add them. I will give a<br />
history<br />
of this problem and explain why it is natural to study it using<br />
algebraic geometry<br />
and representation theory. I will conclude by discussing recent exciting<br />
developments<br />
that explain the second phrase in the title.<br />
<br />
== October 9, 2020, [https://impa.br/en_US/page-pessoas/carolina-araujo/ Carolina Araujo] (IMPA) ==<br />
<br />
(Hosted by Ellenberg)<br />
<br />
== October 23, 2020, [http://www.math.toronto.edu/quastel/ Jeremy Quastel] (University of Toronto) ==<br />
<br />
(Hosted by Gorin)<br />
<br />
== November 6, 2020, [http://math.jhu.edu/~sakellar/ Yiannis Sakellaridis] (Johns Hopkins University)==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
== November 20, 2020, TBA ==<br />
<br />
== December 4, 2020, TBA ==<br />
<br />
<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19869Colloquia2020-09-18T16:15:45Z<p>Vadicgor: /* September 25, 2020, Joseph Landsberg (Texas A&M) */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2020=<br />
<br />
== September 25, 2020, [https://www.math.tamu.edu/~jml/ Joseph Landsberg] (Texas A&M) ==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
'''From theoretic computer science to algebraic geometry: how the<br />
complexity<br />
of matrix multiplication led me to the Hilbert scheme of points.'''<br />
<br />
In 1968 Strassen discovered the way we multiply nxn matrices<br />
(row/column)<br />
is not the most efficient algorithm possible. Subsequent work has led to<br />
the astounding conjecture that as the size n of the matrices grows, it<br />
becomes<br />
almost as easy to multiply matrices as it is to add them. I will give a<br />
history<br />
of this problem and explain why it is natural to study it using<br />
algebraic geometry<br />
and representation theory. I will conclude by discussing recent exciting<br />
developments<br />
that explain the second phrase in the title.<br />
<br />
== October 9, 2020, [https://impa.br/en_US/page-pessoas/carolina-araujo/ Carolina Araujo] (IMPA) ==<br />
<br />
(Hosted by Ellenberg)<br />
<br />
== October 23, 2020, [http://www.math.toronto.edu/quastel/ Jeremy Quastel] (University of Toronto) ==<br />
<br />
(Hosted by Gorin)<br />
<br />
== November 6, 2020, [http://math.jhu.edu/~sakellar/ Yiannis Sakellaridis] (Johns Hopkins University)==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
== November 20, 2020, TBA ==<br />
<br />
== December 4, 2020, TBA ==<br />
<br />
<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19868Colloquia2020-09-18T16:15:34Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2020=<br />
<br />
== September 25, 2020, [https://www.math.tamu.edu/~jml/ Joseph Landsberg] (Texas A&M) ==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
```From theoretic computer science to algebraic geometry: how the<br />
complexity<br />
of matrix multiplication led me to the Hilbert scheme of points.'''<br />
<br />
In 1968 Strassen discovered the way we multiply nxn matrices<br />
(row/column)<br />
is not the most efficient algorithm possible. Subsequent work has led to<br />
the astounding conjecture that as the size n of the matrices grows, it<br />
becomes<br />
almost as easy to multiply matrices as it is to add them. I will give a<br />
history<br />
of this problem and explain why it is natural to study it using<br />
algebraic geometry<br />
and representation theory. I will conclude by discussing recent exciting<br />
developments<br />
that explain the second phrase in the title.<br />
<br />
== October 9, 2020, [https://impa.br/en_US/page-pessoas/carolina-araujo/ Carolina Araujo] (IMPA) ==<br />
<br />
(Hosted by Ellenberg)<br />
<br />
== October 23, 2020, [http://www.math.toronto.edu/quastel/ Jeremy Quastel] (University of Toronto) ==<br />
<br />
(Hosted by Gorin)<br />
<br />
== November 6, 2020, [http://math.jhu.edu/~sakellar/ Yiannis Sakellaridis] (Johns Hopkins University)==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
== November 20, 2020, TBA ==<br />
<br />
== December 4, 2020, TBA ==<br />
<br />
<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Probability_Seminar&diff=19810Probability Seminar2020-09-15T00:29:34Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Fall 2020 =<br />
<br />
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. <br />
<b>We usually end for questions at 3:20 PM.</b><br />
<br />
<b> IMPORTANT: </b> In Fall 2020 the seminar is being run online.<br />
<br />
If you would like to sign up for the email list to receive seminar announcements then please join [https://groups.google.com/a/g-groups.wisc.edu/forum/#!forum/probsem our group].<br />
<br />
== September 17, 2020, [https://www.math.tamu.edu/~bhanin/ Boris Hanin] (Princeton and Texas A&M) ==<br />
<br />
'''Pre-Talk: (1:00pm)'''<br />
<br />
'''Neural Networks for Probabilists''' <br />
<br />
Deep neural networks are a centerpiece in modern machine learning. They are also fascinating probabilistic models, about which much remains unclear. In this pre-talk I will define neural networks, explain how they are used in practice, and give a survey of the big theoretical questions they have raised. If time permits, I will also explain how neural networks are related to a variety of classical areas in probability and mathematical physics, including random matrix theory, optimal transport, and combinatorics of hyperplane arrangements.<br />
<br />
'''Talk: (2:30pm)'''<br />
<br />
'''Effective Theory of Deep Neural Networks''' <br />
<br />
Deep neural networks are often considered to be complicated "black boxes," for which a full systematic analysis is not only out of reach but also impossible. In this talk, which is based on ongoing joint work with Sho Yaida and Daniel Adam Roberts, I will make the opposite claim. Namely, that deep neural networks with random weights and biases are exactly solvable models. Our approach applies to networks at finite width n and large depth L, the regime in which they are used in practice. A key point will be the emergence of a notion of "criticality," which involves a finetuning of model parameters (weight and bias variances). At criticality, neural networks are particularly well-behaved but still exhibit a tension between large values for n and L, with large values of n tending to make neural networks more like Gaussian processes and large values of L amplifying higher cumulants. Our analysis at initialization has many consequences also for networks during after training, which I will discuss if time permits.<br />
<br />
== September 24, 2020, [https://people.ucd.ie/neil.oconnell Neil O'Connell] (Dublin) ==<br />
<br />
'''Some new perspectives on moments of random matrices'''<br />
<br />
The study of `moments' of random matrices (expectations of traces of powers of the matrix) is a rich and interesting subject, with fascinating connections to enumerative geometry, as discovered by Harer and Zagier in the 1980’s. I will give some background on this and then describe some recent work which offers some new perspectives (and new results). This talk is based on joint work with Fabio Deelan Cunden, Francesco Mezzadri and Nick Simm.<br />
<br />
== October 1, 2020, [https://marcusmichelen.org/ Marcus Michelen] ([https://mscs.uic.edu/ UIC]) ==<br />
<br />
'''Roots of random polynomials near the unit circle'''<br />
<br />
It is a well-known (but perhaps surprising) fact that a polynomial with independent random coefficients has most of its roots very close to the unit circle. Using a probabilistic perspective, we understand the behavior of roots of random polynomials exceptionally close to the unit circle and prove several limit theorems; these results resolve several conjectures of Shepp and Vanderbei. We will also discuss how our techniques provide a heuristic, probabilistic explanation for why random polynomials tend to have most roots near the unit circle. Based on joint work with Julian Sahasrabudhe.<br />
<br />
== October 8, 2020, [http://sites.harvard.edu/~sus977/index.html Subhabrata Sen] ([https://statistics.fas.harvard.edu/ Harvard]) ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
== October 15, 2020, [https://math.cornell.edu/philippe-sosoe Philippe Sosoe] (Cornell) ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
==October 22, 2020, [http://www.math.toronto.edu/balint/ Balint Virag] (Toronto) ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
== November 12, 2020, [http://stanford.edu/~ajdunl2/ Alexander Dunlap] ([https://cims.nyu.edu/ NYU Courant Institute]) ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
<br />
[[Past Seminars]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Probability_Seminar&diff=19809Probability Seminar2020-09-15T00:28:50Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Fall 2020 =<br />
<br />
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. <br />
<b>We usually end for questions at 3:20 PM.</b><br />
<br />
<b> IMPORTANT: </b> In Fall 2020 the seminar is being run online.<br />
<br />
If you would like to sign up for the email list to receive seminar announcements then please join [https://groups.google.com/a/g-groups.wisc.edu/forum/#!forum/probsem our group].<br />
<br />
== September 17, 2020, [https://www.math.tamu.edu/~bhanin/ Boris Hanin] (Princeton and Texas A&M) ==<br />
<br />
'''Pre-Talk: (1:00pm)'''<br />
<br />
'''Neural Networks for Probabilists''' <br />
<br />
Deep neural networks are a centerpiece in modern machine learning. They are also fascinating probabilistic models, about which much remains unclear. In this pre-talk I will define neural networks, explain how they are used in practice, and give a survey of the big theoretical questions they have raised. If time permits, I will also explain how neural networks are related to a variety of classical areas in probability and mathematical physics, including random matrix theory, optimal transport, and combinatorics of hyperplane arrangements.<br />
<br />
'''Talk: (2:30pm)'''<br />
<br />
'''Effective Theory of Deep Neural Networks''' <br />
<br />
Deep neural networks are often considered to be complicated "black boxes," for which a full systematic analysis is not only out of reach but also impossible. In this talk, which is based on ongoing joint work with Sho Yaida and Daniel Adam Roberts, I will make the opposite claim. Namely, that deep neural networks with random weights and biases are exactly solvable models. Our approach applies to networks at finite width n and large depth L, the regime in which they are used in practice. A key point will be the emergence of a notion of "criticality," which involves a finetuning of model parameters (weight and bias variances). At criticality, neural networks are particularly well-behaved but still exhibit a tension between large values for n and L, with large values of n tending to make neural networks more like Gaussian processes and large values of L amplifying higher cumulants. Our analysis at initialization has many consequences also for networks during after training, which I will discuss if time permits.<br />
<br />
== September 24, 2020, [https://people.ucd.ie/neil.oconnell Neil O'Connell] (Dublin) ==<br />
<br />
'''Some new perspectives on moments of random matrices'''<br />
<br />
The study of `moments' of random matrices (expectations of traces of powers of the matrix) is a rich and interesting subject, with fascinating connections to enumerative geometry, as discovered by Harer and Zagier in the 1980’s. I will give some background on this and then describe some recent work which offers some new perspectives (and new results). This talk is based on joint work with Fabio Deelan Cunden, Francesco Mezzadri and Nick Simm.<br />
<br />
== October 1, 2020, [https://marcusmichelen.org/ Marcus Michelen], [https://mscs.uic.edu/ UIC] ==<br />
<br />
'''Roots of random polynomials near the unit circle'''<br />
<br />
It is a well-known (but perhaps surprising) fact that a polynomial with independent random coefficients has most of its roots very close to the unit circle. Using a probabilistic perspective, we understand the behavior of roots of random polynomials exceptionally close to the unit circle and prove several limit theorems; these results resolve several conjectures of Shepp and Vanderbei. We will also discuss how our techniques provide a heuristic, probabilistic explanation for why random polynomials tend to have most roots near the unit circle. Based on joint work with Julian Sahasrabudhe.<br />
<br />
== October 8, 2020, [http://sites.harvard.edu/~sus977/index.html Subhabrata Sen], [https://statistics.fas.harvard.edu/ Harvard] ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
== October 15, 2020, [https://math.cornell.edu/philippe-sosoe Philippe Sosoe], (Cornell) ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
==October 22, 2020, [http://www.math.toronto.edu/balint/ Balint Virag], (Toronto) ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
== November 12, 2020, [http://stanford.edu/~ajdunl2/ Alexander Dunlap], [https://cims.nyu.edu/ NYU Courant Institute] ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
<br />
[[Past Seminars]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Probability_Seminar&diff=19804Probability Seminar2020-09-14T17:59:07Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Fall 2020 =<br />
<br />
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. <br />
<b>We usually end for questions at 3:20 PM.</b><br />
<br />
<b> IMPORTANT: </b> In Fall 2020 the seminar is being run online.<br />
<br />
If you would like to sign up for the email list to receive seminar announcements then please join [https://groups.google.com/a/g-groups.wisc.edu/forum/#!forum/probsem our group].<br />
<br />
== September 17, 2020, [https://www.math.tamu.edu/~bhanin/ Boris Hanin] (Princeton and Texas A&M) ==<br />
<br />
'''Pre-Talk: (1:00pm)'''<br />
<br />
'''Neural Networks for Probabilists''' <br />
<br />
Deep neural networks are a centerpiece in modern machine learning. They are also fascinating probabilistic models, about which much remains unclear. In this pre-talk I will define neural networks, explain how they are used in practice, and give a survey of the big theoretical questions they have raised. If time permits, I will also explain how neural networks are related to a variety of classical areas in probability and mathematical physics, including random matrix theory, optimal transport, and combinatorics of hyperplane arrangements.<br />
<br />
'''Talk: (2:30pm)'''<br />
<br />
'''Effective Theory of Deep Neural Networks''' <br />
<br />
Deep neural networks are often considered to be complicated "black boxes," for which a full systematic analysis is not only out of reach but also impossible. In this talk, which is based on ongoing joint work with Sho Yaida and Daniel Adam Roberts, I will make the opposite claim. Namely, that deep neural networks with random weights and biases are exactly solvable models. Our approach applies to networks at finite width n and large depth L, the regime in which they are used in practice. A key point will be the emergence of a notion of "criticality," which involves a finetuning of model parameters (weight and bias variances). At criticality, neural networks are particularly well-behaved but still exhibit a tension between large values for n and L, with large values of n tending to make neural networks more like Gaussian processes and large values of L amplifying higher cumulants. Our analysis at initialization has many consequences also for networks during after training, which I will discuss if time permits.<br />
<br />
== September 24, 2020, [https://people.ucd.ie/neil.oconnell Neil O'Connell] (Dublin) ==<br />
<br />
'''Some new perspectives on moments of random matrices'''<br />
<br />
The study of `moments' of random matrices (expectations of traces of powers of the matrix) is a rich and interesting subject, with fascinating connections to enumerative geometry, as discovered by Harer and Zagier in the 1980’s. I will give some background on this and then describe some recent work which offers some new perspectives (and new results). This talk is based on joint work with Fabio Deelan Cunden, Francesco Mezzadri and Nick Simm.<br />
<br />
== October 1, 2020, [https://marcusmichelen.org/ Marcus Michelen], [https://mscs.uic.edu/ UIC] ==<br />
<br />
'''Roots of random polynomials near the unit circle'''<br />
<br />
It is a well-known (but perhaps surprising) fact that a polynomial with independent random coefficients has most of its roots very close to the unit circle. Using a probabilistic perspective, we understand the behavior of roots of random polynomials exceptionally close to the unit circle and prove several limit theorems; these results resolve several conjectures of Shepp and Vanderbei. We will also discuss how our techniques provide a heuristic, probabilistic explanation for why random polynomials tend to have most roots near the unit circle. Based on joint work with Julian Sahasrabudhe.<br />
<br />
== October 8, 2020, [http://sites.harvard.edu/~sus977/index.html Subhabrata Sen], [https://statistics.fas.harvard.edu/ Harvard] ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
== November 12, 2020, [http://stanford.edu/~ajdunl2/ Alexander Dunlap], [https://cims.nyu.edu/ NYU Courant Institute] ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
<br />
[[Past Seminars]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Probability_Seminar&diff=19803Probability Seminar2020-09-14T17:58:49Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Fall 2020 =<br />
<br />
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. <br />
<b>We usually end for questions at 3:20 PM.</b><br />
<br />
<b> IMPORTANT: </b> In Fall 2020 the seminar is being run online.<br />
<br />
If you would like to sign up for the email list to receive seminar announcements then please join [https://groups.google.com/a/g-groups.wisc.edu/forum/#!forum/probsem our group].<br />
<br />
== September 17, 2020, [https://www.math.tamu.edu/~bhanin/ Boris Hanin] (Princeton and Texas A&M) ==<br />
<br />
'''Pre-Talk (1:00pm):'''<br />
<br />
'''Neural Networks for Probabilists''' <br />
<br />
Deep neural networks are a centerpiece in modern machine learning. They are also fascinating probabilistic models, about which much remains unclear. In this pre-talk I will define neural networks, explain how they are used in practice, and give a survey of the big theoretical questions they have raised. If time permits, I will also explain how neural networks are related to a variety of classical areas in probability and mathematical physics, including random matrix theory, optimal transport, and combinatorics of hyperplane arrangements.<br />
<br />
'''Talk: (2:30pm)'''<br />
<br />
'''Effective Theory of Deep Neural Networks''' <br />
<br />
Deep neural networks are often considered to be complicated "black boxes," for which a full systematic analysis is not only out of reach but also impossible. In this talk, which is based on ongoing joint work with Sho Yaida and Daniel Adam Roberts, I will make the opposite claim. Namely, that deep neural networks with random weights and biases are exactly solvable models. Our approach applies to networks at finite width n and large depth L, the regime in which they are used in practice. A key point will be the emergence of a notion of "criticality," which involves a finetuning of model parameters (weight and bias variances). At criticality, neural networks are particularly well-behaved but still exhibit a tension between large values for n and L, with large values of n tending to make neural networks more like Gaussian processes and large values of L amplifying higher cumulants. Our analysis at initialization has many consequences also for networks during after training, which I will discuss if time permits.<br />
<br />
== September 24, 2020, [https://people.ucd.ie/neil.oconnell Neil O'Connell] (Dublin) ==<br />
<br />
'''Some new perspectives on moments of random matrices'''<br />
<br />
The study of `moments' of random matrices (expectations of traces of powers of the matrix) is a rich and interesting subject, with fascinating connections to enumerative geometry, as discovered by Harer and Zagier in the 1980’s. I will give some background on this and then describe some recent work which offers some new perspectives (and new results). This talk is based on joint work with Fabio Deelan Cunden, Francesco Mezzadri and Nick Simm.<br />
<br />
== October 1, 2020, [https://marcusmichelen.org/ Marcus Michelen], [https://mscs.uic.edu/ UIC] ==<br />
<br />
'''Roots of random polynomials near the unit circle'''<br />
<br />
It is a well-known (but perhaps surprising) fact that a polynomial with independent random coefficients has most of its roots very close to the unit circle. Using a probabilistic perspective, we understand the behavior of roots of random polynomials exceptionally close to the unit circle and prove several limit theorems; these results resolve several conjectures of Shepp and Vanderbei. We will also discuss how our techniques provide a heuristic, probabilistic explanation for why random polynomials tend to have most roots near the unit circle. Based on joint work with Julian Sahasrabudhe.<br />
<br />
== October 8, 2020, [http://sites.harvard.edu/~sus977/index.html Subhabrata Sen], [https://statistics.fas.harvard.edu/ Harvard] ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
== November 12, 2020, [http://stanford.edu/~ajdunl2/ Alexander Dunlap], [https://cims.nyu.edu/ NYU Courant Institute] ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
<br />
[[Past Seminars]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Probability_Seminar&diff=19802Probability Seminar2020-09-14T17:57:48Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Fall 2020 =<br />
<br />
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. <br />
<b>We usually end for questions at 3:20 PM.</b><br />
<br />
<b> IMPORTANT: </b> In Fall 2020 the seminar is being run online.<br />
<br />
If you would like to sign up for the email list to receive seminar announcements then please join [https://groups.google.com/a/g-groups.wisc.edu/forum/#!forum/probsem our group].<br />
<br />
== September 17, 2020, [https://www.math.tamu.edu/~bhanin/ Boris Hanin] (Princeton and Texas A&M) ==<br />
<br />
'''Pre-Talk (1:00pm):'''<br />
<br />
Title: '''Neural Networks for Probabilists''' <br />
<br />
Abstract: Deep neural networks are a centerpiece in modern machine learning. They are also fascinating probabilistic models, about which much remains unclear. In this pre-talk I will define neural networks, explain how they are used in practice, and give a survey of the big theoretical questions they have raised. If time permits, I will also explain how neural networks are related to a variety of classical areas in probability and mathematical physics, including random matrix theory, optimal transport, and combinatorics of hyperplane arrangements.<br />
<br />
'''Talk: (2:30pm)'''<br />
<br />
Title: '''Effective Theory of Deep Neural Networks''' <br />
<br />
Abstract: Deep neural networks are often considered to be complicated "black boxes," for which a full systematic analysis is not only out of reach but also impossible. In this talk, which is based on ongoing joint work with Sho Yaida and Daniel Adam Roberts, I will make the opposite claim. Namely, that deep neural networks with random weights and biases are exactly solvable models. Our approach applies to networks at finite width n and large depth L, the regime in which they are used in practice. A key point will be the emergence of a notion of "criticality," which involves a finetuning of model parameters (weight and bias variances). At criticality, neural networks are particularly well-behaved but still exhibit a tension between large values for n and L, with large values of n tending to make neural networks more like Gaussian processes and large values of L amplifying higher cumulants. Our analysis at initialization has many consequences also for networks during after training, which I will discuss if time permits.<br />
<br />
== September 24, 2020, [https://people.ucd.ie/neil.oconnell Neil O'Connell] (Dublin) ==<br />
<br />
Title: '''Some new perspectives on moments of random matrices'''<br />
<br />
Abstract: The study of `moments' of random matrices (expectations of traces of powers of the matrix) is a rich and interesting subject, with fascinating connections to enumerative geometry, as discovered by Harer and Zagier in the 1980’s. I will give some background on this and then describe some recent work which offers some new perspectives (and new results). This talk is based on joint work with Fabio Deelan Cunden, Francesco Mezzadri and Nick Simm.<br />
<br />
== October 1, 2020, [https://marcusmichelen.org/ Marcus Michelen], [https://mscs.uic.edu/ UIC] ==<br />
<br />
Title: '''Roots of random polynomials near the unit circle'''<br />
<br />
Abstract: It is a well-known (but perhaps surprising) fact that a polynomial with independent random coefficients has most of its roots very close to the unit circle. Using a probabilistic perspective, we understand the behavior of roots of random polynomials exceptionally close to the unit circle and prove several limit theorems; these results resolve several conjectures of Shepp and Vanderbei. We will also discuss how our techniques provide a heuristic, probabilistic explanation for why random polynomials tend to have most roots near the unit circle. Based on joint work with Julian Sahasrabudhe.<br />
<br />
== October 8, 2020, [http://sites.harvard.edu/~sus977/index.html Subhabrata Sen], [https://statistics.fas.harvard.edu/ Harvard] ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
== November 12, 2020, [http://stanford.edu/~ajdunl2/ Alexander Dunlap], [https://cims.nyu.edu/ NYU Courant Institute] ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
<br />
[[Past Seminars]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19646Colloquia2020-09-04T02:35:50Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2020=<br />
<br />
== September 25, 2020, [https://www.math.tamu.edu/~jml/ Joseph Landsberg] (Texas A&M) ==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
== October 9, 2020, [https://impa.br/en_US/page-pessoas/carolina-araujo/ Carolina Araujo] (IMPA) ==<br />
<br />
(Hosted by Ellenberg)<br />
<br />
== October 23, 2020, [http://www.math.toronto.edu/quastel/ Jeremy Quastel] (University of Toronto) ==<br />
<br />
(Hosted by Gorin)<br />
<br />
== November 6, 2020, [http://math.jhu.edu/~sakellar/ Yiannis Sakellaridis] (Johns Hopkins University)==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
== November 20, 2020, TBA ==<br />
<br />
== December 4, 2020, TBA ==<br />
<br />
<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19645Colloquia2020-09-04T02:35:30Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2020=<br />
<br />
== September 25, 2020, [https://www.math.tamu.edu/~jml/ Joseph Landsberg] (Texas A&M) ==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
== October 9, 2020, [https://impa.br/en_US/page-pessoas/carolina-araujo/ Carolina Araujo] (IMPA) ==<br />
<br />
== October 23, 2020, [http://www.math.toronto.edu/quastel/ Jeremy Quastel] (University of Toronto) ==<br />
<br />
(Hosted by Gorin)<br />
<br />
== November 6, 2020, [http://math.jhu.edu/~sakellar/ Yiannis Sakellaridis] (Johns Hopkins University)==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
== November 20, 2020, TBA ==<br />
<br />
== December 4, 2020, TBA ==<br />
<br />
<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19628Colloquia2020-09-03T04:38:21Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2020=<br />
<br />
== September 25, 2020, [https://www.math.tamu.edu/~jml/ Joseph Landsberg] (Texas A&M) ==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
== October 9, 2020, TBA ==<br />
<br />
== October 23, 2020, [http://www.math.toronto.edu/quastel/ Jeremy Quastel] (University of Toronto) ==<br />
<br />
(Hosted by Gorin)<br />
<br />
== November 6, 2020, [http://math.jhu.edu/~sakellar/ Yiannis Sakellaridis] (Johns Hopkins University)==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
== November 20, 2020, TBA ==<br />
<br />
== December 4, 2020, TBA ==<br />
<br />
<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Graduate_student_reading_seminar&diff=19624Graduate student reading seminar2020-09-01T19:35:49Z<p>Vadicgor: </p>
<hr />
<div>(... in probability)<br />
<br />
[https://groups.google.com/a/g-groups.wisc.edu/forum/#!forum/grad_prob_seminar Email list] <br />
<br />
==2020 Fall==<br />
<br />
<br />
==2020 Spring==<br />
<br />
Tuesday 2:30pm, 901 Van Vleck<br />
<br />
2/4, 2/11: Edwin<br />
<br />
2/18, 2/25: Chaojie<br />
<br />
3/3. 3/10: Yu Sun<br />
<br />
3/24, 3/31: Tony<br />
<br />
4/7, 4/14: Tung<br />
<br />
4/21, 4/28: Tung<br />
<br />
==2019 Fall==<br />
<br />
Tuesday 2:30pm, 901 Van Vleck<br />
<br />
9/24, 10/1: Xiao<br />
<br />
10/8, 10/15: Jakwang<br />
<br />
10/22, 10/29: Evan<br />
<br />
11/5, 11/12: Chaojie<br />
<br />
12/3, 12/10: Tung<br />
<br />
==2019 Spring==<br />
<br />
Tuesday 2:30pm, 901 Van Vleck<br />
<br />
2/5: Timo<br />
<br />
2/12, 2/19: Evan<br />
<br />
2/26, 3/5: Chaojie<br />
<br />
3/12, 3/26: Kurt<br />
<br />
4/2, 4/9: Yu<br />
<br />
4/16, 4/23: Max<br />
<br />
4/30, 5/7: Xiao<br />
<br />
==2018 Fall==<br />
<br />
Tuesday 2:30pm, 901 Van Vleck<br />
<br />
<br />
The topic this semester is large deviation theory. Send me (BV) an email, if you want access to the shared Box folder with some reading material. <br />
<br />
<br />
9/25, 10/2: Dae Han<br />
<br />
10/9, 10/16: Kurt<br />
<br />
10/23, 10/30: Jane Davis<br />
<br />
11/6, 11/13: Brandon Legried <br />
<br />
11/20, 11/27: Shuqi Yu<br />
<br />
12/4, 12/11: Yun Li<br />
<br />
==2018 Spring==<br />
<br />
Tuesday 2:30pm, B135 Van Vleck<br />
<br />
<br />
Preliminary schedule:<br />
<br />
2/20, 2/27: Yun<br />
<br />
3/6, 3/13: Greg<br />
<br />
3/20, 4/3: Yu<br />
<br />
4/10, 4/17: Shuqi<br />
<br />
4/24, 5/1: Tony<br />
<br />
==2017 Fall==<br />
<br />
Tuesday 2:30pm, 214 Ingraham Hall<br />
<br />
<br />
Preliminary schedule: <br />
<br />
9/26, 10/3: Hans<br />
<br />
10/10, 10/17: Guo<br />
<br />
10/24, 10/31: Chaoji<br />
<br />
11/7, 11/14: Yun <br />
<br />
11/21, 11/28: Kurt<br />
<br />
12/5, 12/12: Christian<br />
<br />
<br />
<br />
<br />
==2017 Spring==<br />
<br />
Tuesday 2:25pm, B211<br />
<br />
1/31, 2/7: Fan<br />
<br />
I will talk about the Hanson-Wright inequality, which is a large deviation estimate for random variable of the form X^* A X, where X is a random vector with independent subgaussian entries and A is an arbitrary deterministic matrix. In the first talk, I will present a beautiful proof given by Mark Rudelson and Roman Vershynin. In the second talk, I will talk about some applications of this inequality.<br />
<br />
Reference: M. Rudelson and R. Vershynin, Hanson-Wright inequality and sub-gaussian concentration, Electron. Commun. Probab. Volume 18 (2013).<br />
<br />
3/7, 3/14 : Jinsu<br />
<br />
Title : Donsker's Theorem and its application.<br />
Donsker's Theorem roughly says normalized random walk with linear interpolation on time interval [0,1] weakly converges to the Brownian motion B[0,1] in C([0,1]). It is sometimes called Donsker's invariance principle or the functional central limit theorem. I will show main ideas for the proof of this theorem tomorrow and show a couple of applications in my 2nd talk.<br />
<br />
Reference : https://www.math.utah.edu/~davar/ps-pdf-files/donsker.pdf<br />
<br />
==2016 Fall==<br />
<br />
9/27 Daniele<br />
<br />
Stochastic reaction networks.<br />
<br />
Stochastic reaction networks are continuous time Markov chain models used primarily in biochemistry. I will define them, prove some results that connect them to related deterministic models and introduce some open questions. <br />
<br />
10/4 Jessica<br />
<br />
10/11, 10/18: Dae Han<br />
<br />
10/25, 11/1: Jinsu<br />
<br />
Coupling of Markov processes.<br />
<br />
When we have two distributions on same probability space, we can think of a pair whose marginal probability is each of two distributions.<br />
This pairing can be used to estimate the total variation distance between two distributions. This idea is called coupling method.<br />
I am going to introduce basic concepts,ideas and applications of coupling for Markov processes.<br />
<br />
Links of References<br />
<br />
http://pages.uoregon.edu/dlevin/MARKOV/markovmixing.pdf<br />
<br />
http://websites.math.leidenuniv.nl/probability/lecturenotes/CouplingLectures.pdf<br />
<br />
11/8, 11/15: Hans<br />
<br />
11/22, 11/29: Keith<br />
<br />
Surprisingly Determinental: DPPs and some asymptotics of ASEP <br />
<br />
I'll be reading and presenting some recent papers of Alexei Borodin and a few collaborators which have uncovered certain equivalences between determinental point processes and non-determinental processes.<br />
<br />
<br />
==2016 Spring==<br />
<br />
Tuesday, 2:25pm, B321 Van Vleck<br />
<br />
<br />
3/29, 4/5: Fan Yang<br />
<br />
I will talk about the ergodic decomposition theorem (EDT). More specifically, given a compact metric space X and a continuous transformation T on it, the theorem shows that any T-invariant measure on X can be decomposed into a convex combination of ergodic measures. In the first talk I introduced the EDT and some related facts. In the second talk, I will talk about the conditional measures, and prove that the ergodic measures in EDT are indeed the conditional measures.<br />
<br />
<br />
2/16 : Jinsu<br />
<br />
Lyapunov function for Markov Processes.<br />
<br />
For ODE, we can show stability of the trajectory using Lyapunov functions.<br />
<br />
There is an analogy for Markov Processes. I'd like to talk about the existence of stationary distribution with Lyapunov function.<br />
<br />
In some cases, it is also possible to show the rate of convergence to the stationary distribution.<br />
<br />
==2015 Fall==<br />
<br />
This semester we will focus on tools and methods.<br />
<br />
[https://www.math.wisc.edu/wiki/images/a/ac/Reading_seminar_2015.pdf Seminar notes] ([https://www.dropbox.com/s/f4km7pevwfb1vbm/Reading%20seminar%202015.tex?dl=1 tex file], [https://www.dropbox.com/s/lg7kcgyf3nsukbx/Reading_seminar_2015.bib?dl=1 bib file])<br />
<br />
9/15, 9/22: Elnur<br />
<br />
I will talk about large deviation theory and its applications. For the first talk, my plan is to introduce Gartner-Ellis theorem and show a few applications of it to finite state discrete time Markov chains.<br />
<br />
9/29, 10/6, 10/13 :Dae Han<br />
<br />
10/20, 10/27, 11/3: Jessica<br />
<br />
I will first present an overview of concentration of measure and concentration inequalities with a focus on the connection with related topics in analysis and geometry. Then, I will present Log-Sobolev inequalities and their connection to concentration of measure. <br />
<br />
11/10, 11/17: Hao Kai<br />
<br />
11/24, 12/1, 12/8, 12/15: Chris<br />
<br />
: <br />
<br />
<br />
<br />
<br />
<br />
2016 Spring:<br />
<br />
2/2, 2/9: Louis<br />
<br />
<br />
2/16, 2/23: Jinsu<br />
<br />
3/1, 3/8: Hans<br />
<br />
==2015 Spring==<br />
<br />
<br />
2/3, 2/10: Scott<br />
<br />
An Introduction to Entropy for Random Variables<br />
<br />
In these lectures I will introduce entropy for random variables and present some simple, finite state-space, examples to gain some intuition. We will prove the <br />
MacMillan Theorem using entropy and the law of large numbers. Then I will introduce relative entropy and prove the Markov Chain Convergence Theorem. Finally I will <br />
define entropy for a discrete time process. The lecture notes can be found at http://www.math.wisc.edu/~shottovy/EntropyLecture.pdf.<br />
<br />
2/17, 2/24: Dae Han<br />
<br />
3/3, 3/10: Hans<br />
<br />
3/17, 3/24: In Gun<br />
<br />
4/7, 4/14: Jinsu<br />
<br />
4/21, 4/28: Chris N.<br />
<br />
<br />
<br />
<br />
<br />
<br />
==2014 Fall==<br />
<br />
9/23: Dave<br />
<br />
I will go over Mike Giles’ 2008 paper “Multi-level Monte Carlo path simulation.” This paper introduced a new Monte Carlo method to approximate expectations of SDEs (driven by Brownian motions) that is significantly more efficient than what was the state of the art. This work opened up a whole new field in the numerical analysis of stochastic processes as the basic idea is quite flexible and has found a variety of applications including SDEs driven by Brownian motions, Levy-driven SDEs, SPDEs, and models from biology<br />
<br />
9/30: Benedek<br />
<br />
A very quick introduction to Stein's method. <br />
<br />
I will give a brief introduction to Stein's method, mostly based on the the first couple of sections of the following survey article:<br />
<br />
Ross, N. (2011). Fundamentals of Stein’s method. Probability Surveys, 8, 210-293. <br />
<br />
The following webpage has a huge collection of resources if you want to go deeper: https://sites.google.com/site/yvikswan/about-stein-s-method<br />
<br />
<br />
Note that the Midwest Probability Colloquium (http://www.math.northwestern.edu/mwp/) will have a tutorial program on Stein's method this year. <br />
<br />
10/7, 10/14: Chris J.<br />
[http://www.math.wisc.edu/~janjigia/research/MartingaleProblemNotes.pdf An introduction to the (local) martingale problem.]<br />
<br />
<br />
10/21, 10/28: Dae Han<br />
<br />
11/4, 11/11: Elnur<br />
<br />
11/18, 11/25: Chris N. Free Probability with an emphasis on C* and Von Neumann Algebras<br />
<br />
12/2, 12/9: Yun Zhai<br />
<br />
==2014 Spring==<br />
<br />
<br />
1/28: Greg<br />
<br />
2/04, 2/11: Scott <br />
<br />
[http://www.math.wisc.edu/~shottovy/BLT.pdf Reflected Brownian motion, Occupation time, and applications.] <br />
<br />
2/18: Phil-- Examples of structure results in probability theory.<br />
<br />
2/25, 3/4: Beth-- Derivative estimation for discrete time Markov chains<br />
<br />
3/11, 3/25: Chris J [http://www.math.wisc.edu/~janjigia/research/stationarytalk.pdf Some classical results on stationary distributions of Markov processes]<br />
<br />
4/1, 4/8: Chris N <br />
<br />
4/15, 4/22: Yu Sun<br />
<br />
4/29. 5/6: Diane<br />
<br />
==2013 Fall==<br />
<br />
9/24, 10/1: Chris<br />
[http://www.math.wisc.edu/~janjigia/research/metastabilitytalk.pdf A light introduction to metastability]<br />
<br />
10/8, Dae Han<br />
Majoring multiplicative cascades for directed polymers in random media<br />
<br />
10/15, 10/22: no reading seminar<br />
<br />
10/29, 11/5: Elnur<br />
Limit fluctuations of last passage times <br />
<br />
11/12: Yun<br />
Helffer-Sjostrand representation and Brascamp-Lieb inequality for stochastic interface models<br />
<br />
11/19, 11/26: Yu Sun<br />
<br />
12/3, 12/10: Jason<br />
<br />
==2013 Spring==<br />
<br />
2/13: Elnur <br />
<br />
Young diagrams, RSK correspondence, corner growth models, distribution of last passage times. <br />
<br />
2/20: Elnur<br />
<br />
2/27: Chris<br />
<br />
A brief introduction to enlargement of filtration and the Dufresne identity<br />
[http://www.math.wisc.edu/~janjigia/research/Presentation%20Notes.pdf Notes]<br />
<br />
3/6: Chris<br />
<br />
3/13: Dae Han<br />
<br />
An introduction to random polymers<br />
<br />
3/20: Dae Han<br />
<br />
Directed polymers in a random environment: path localization and strong disorder<br />
<br />
4/3: Diane<br />
<br />
Scale and Speed for honest 1 dimensional diffusions<br />
<br />
References: <br><br />
Rogers & Williams - Diffusions, Markov Processes and Martingales <br><br />
Ito & McKean - Diffusion Processes and their Sample Paths <br><br />
Breiman - Probability <br><br />
http://www.statslab.cam.ac.uk/~beresty/Articles/diffusions.pdf<br />
<br />
4/10: Diane<br />
<br />
4/17: Yun<br />
<br />
Introduction to stochastic interface models<br />
<br />
4/24: Yun<br />
<br />
Dynamics and Gaussian equilibrium sytems<br />
<br />
5/1: This reading seminar will be shifted because of a probability seminar.<br />
<br />
<br />
5/8: Greg, Maso<br />
<br />
The Bethe ansatz vs. The Replica Trick. This lecture is an overview of the two <br />
approaches. See [http://arxiv.org/abs/1212.2267] for a nice overview.<br />
<br />
5/15: Greg, Maso<br />
<br />
Rigorous use of the replica trick.</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Graduate_student_reading_seminar&diff=19623Graduate student reading seminar2020-09-01T19:35:39Z<p>Vadicgor: </p>
<hr />
<div>(... in probability)<br />
<br />
<br />
[https://groups.google.com/a/g-groups.wisc.edu/forum/#!forum/grad_prob_seminar Email list] <br />
<br />
==2020 Fall==<br />
<br />
<br />
==2020 Spring==<br />
<br />
Tuesday 2:30pm, 901 Van Vleck<br />
<br />
2/4, 2/11: Edwin<br />
<br />
2/18, 2/25: Chaojie<br />
<br />
3/3. 3/10: Yu Sun<br />
<br />
3/24, 3/31: Tony<br />
<br />
4/7, 4/14: Tung<br />
<br />
4/21, 4/28: Tung<br />
<br />
==2019 Fall==<br />
<br />
Tuesday 2:30pm, 901 Van Vleck<br />
<br />
9/24, 10/1: Xiao<br />
<br />
10/8, 10/15: Jakwang<br />
<br />
10/22, 10/29: Evan<br />
<br />
11/5, 11/12: Chaojie<br />
<br />
12/3, 12/10: Tung<br />
<br />
==2019 Spring==<br />
<br />
Tuesday 2:30pm, 901 Van Vleck<br />
<br />
2/5: Timo<br />
<br />
2/12, 2/19: Evan<br />
<br />
2/26, 3/5: Chaojie<br />
<br />
3/12, 3/26: Kurt<br />
<br />
4/2, 4/9: Yu<br />
<br />
4/16, 4/23: Max<br />
<br />
4/30, 5/7: Xiao<br />
<br />
==2018 Fall==<br />
<br />
Tuesday 2:30pm, 901 Van Vleck<br />
<br />
<br />
The topic this semester is large deviation theory. Send me (BV) an email, if you want access to the shared Box folder with some reading material. <br />
<br />
<br />
9/25, 10/2: Dae Han<br />
<br />
10/9, 10/16: Kurt<br />
<br />
10/23, 10/30: Jane Davis<br />
<br />
11/6, 11/13: Brandon Legried <br />
<br />
11/20, 11/27: Shuqi Yu<br />
<br />
12/4, 12/11: Yun Li<br />
<br />
==2018 Spring==<br />
<br />
Tuesday 2:30pm, B135 Van Vleck<br />
<br />
<br />
Preliminary schedule:<br />
<br />
2/20, 2/27: Yun<br />
<br />
3/6, 3/13: Greg<br />
<br />
3/20, 4/3: Yu<br />
<br />
4/10, 4/17: Shuqi<br />
<br />
4/24, 5/1: Tony<br />
<br />
==2017 Fall==<br />
<br />
Tuesday 2:30pm, 214 Ingraham Hall<br />
<br />
<br />
Preliminary schedule: <br />
<br />
9/26, 10/3: Hans<br />
<br />
10/10, 10/17: Guo<br />
<br />
10/24, 10/31: Chaoji<br />
<br />
11/7, 11/14: Yun <br />
<br />
11/21, 11/28: Kurt<br />
<br />
12/5, 12/12: Christian<br />
<br />
<br />
<br />
<br />
==2017 Spring==<br />
<br />
Tuesday 2:25pm, B211<br />
<br />
1/31, 2/7: Fan<br />
<br />
I will talk about the Hanson-Wright inequality, which is a large deviation estimate for random variable of the form X^* A X, where X is a random vector with independent subgaussian entries and A is an arbitrary deterministic matrix. In the first talk, I will present a beautiful proof given by Mark Rudelson and Roman Vershynin. In the second talk, I will talk about some applications of this inequality.<br />
<br />
Reference: M. Rudelson and R. Vershynin, Hanson-Wright inequality and sub-gaussian concentration, Electron. Commun. Probab. Volume 18 (2013).<br />
<br />
3/7, 3/14 : Jinsu<br />
<br />
Title : Donsker's Theorem and its application.<br />
Donsker's Theorem roughly says normalized random walk with linear interpolation on time interval [0,1] weakly converges to the Brownian motion B[0,1] in C([0,1]). It is sometimes called Donsker's invariance principle or the functional central limit theorem. I will show main ideas for the proof of this theorem tomorrow and show a couple of applications in my 2nd talk.<br />
<br />
Reference : https://www.math.utah.edu/~davar/ps-pdf-files/donsker.pdf<br />
<br />
==2016 Fall==<br />
<br />
9/27 Daniele<br />
<br />
Stochastic reaction networks.<br />
<br />
Stochastic reaction networks are continuous time Markov chain models used primarily in biochemistry. I will define them, prove some results that connect them to related deterministic models and introduce some open questions. <br />
<br />
10/4 Jessica<br />
<br />
10/11, 10/18: Dae Han<br />
<br />
10/25, 11/1: Jinsu<br />
<br />
Coupling of Markov processes.<br />
<br />
When we have two distributions on same probability space, we can think of a pair whose marginal probability is each of two distributions.<br />
This pairing can be used to estimate the total variation distance between two distributions. This idea is called coupling method.<br />
I am going to introduce basic concepts,ideas and applications of coupling for Markov processes.<br />
<br />
Links of References<br />
<br />
http://pages.uoregon.edu/dlevin/MARKOV/markovmixing.pdf<br />
<br />
http://websites.math.leidenuniv.nl/probability/lecturenotes/CouplingLectures.pdf<br />
<br />
11/8, 11/15: Hans<br />
<br />
11/22, 11/29: Keith<br />
<br />
Surprisingly Determinental: DPPs and some asymptotics of ASEP <br />
<br />
I'll be reading and presenting some recent papers of Alexei Borodin and a few collaborators which have uncovered certain equivalences between determinental point processes and non-determinental processes.<br />
<br />
<br />
==2016 Spring==<br />
<br />
Tuesday, 2:25pm, B321 Van Vleck<br />
<br />
<br />
3/29, 4/5: Fan Yang<br />
<br />
I will talk about the ergodic decomposition theorem (EDT). More specifically, given a compact metric space X and a continuous transformation T on it, the theorem shows that any T-invariant measure on X can be decomposed into a convex combination of ergodic measures. In the first talk I introduced the EDT and some related facts. In the second talk, I will talk about the conditional measures, and prove that the ergodic measures in EDT are indeed the conditional measures.<br />
<br />
<br />
2/16 : Jinsu<br />
<br />
Lyapunov function for Markov Processes.<br />
<br />
For ODE, we can show stability of the trajectory using Lyapunov functions.<br />
<br />
There is an analogy for Markov Processes. I'd like to talk about the existence of stationary distribution with Lyapunov function.<br />
<br />
In some cases, it is also possible to show the rate of convergence to the stationary distribution.<br />
<br />
==2015 Fall==<br />
<br />
This semester we will focus on tools and methods.<br />
<br />
[https://www.math.wisc.edu/wiki/images/a/ac/Reading_seminar_2015.pdf Seminar notes] ([https://www.dropbox.com/s/f4km7pevwfb1vbm/Reading%20seminar%202015.tex?dl=1 tex file], [https://www.dropbox.com/s/lg7kcgyf3nsukbx/Reading_seminar_2015.bib?dl=1 bib file])<br />
<br />
9/15, 9/22: Elnur<br />
<br />
I will talk about large deviation theory and its applications. For the first talk, my plan is to introduce Gartner-Ellis theorem and show a few applications of it to finite state discrete time Markov chains.<br />
<br />
9/29, 10/6, 10/13 :Dae Han<br />
<br />
10/20, 10/27, 11/3: Jessica<br />
<br />
I will first present an overview of concentration of measure and concentration inequalities with a focus on the connection with related topics in analysis and geometry. Then, I will present Log-Sobolev inequalities and their connection to concentration of measure. <br />
<br />
11/10, 11/17: Hao Kai<br />
<br />
11/24, 12/1, 12/8, 12/15: Chris<br />
<br />
: <br />
<br />
<br />
<br />
<br />
<br />
2016 Spring:<br />
<br />
2/2, 2/9: Louis<br />
<br />
<br />
2/16, 2/23: Jinsu<br />
<br />
3/1, 3/8: Hans<br />
<br />
==2015 Spring==<br />
<br />
<br />
2/3, 2/10: Scott<br />
<br />
An Introduction to Entropy for Random Variables<br />
<br />
In these lectures I will introduce entropy for random variables and present some simple, finite state-space, examples to gain some intuition. We will prove the <br />
MacMillan Theorem using entropy and the law of large numbers. Then I will introduce relative entropy and prove the Markov Chain Convergence Theorem. Finally I will <br />
define entropy for a discrete time process. The lecture notes can be found at http://www.math.wisc.edu/~shottovy/EntropyLecture.pdf.<br />
<br />
2/17, 2/24: Dae Han<br />
<br />
3/3, 3/10: Hans<br />
<br />
3/17, 3/24: In Gun<br />
<br />
4/7, 4/14: Jinsu<br />
<br />
4/21, 4/28: Chris N.<br />
<br />
<br />
<br />
<br />
<br />
<br />
==2014 Fall==<br />
<br />
9/23: Dave<br />
<br />
I will go over Mike Giles’ 2008 paper “Multi-level Monte Carlo path simulation.” This paper introduced a new Monte Carlo method to approximate expectations of SDEs (driven by Brownian motions) that is significantly more efficient than what was the state of the art. This work opened up a whole new field in the numerical analysis of stochastic processes as the basic idea is quite flexible and has found a variety of applications including SDEs driven by Brownian motions, Levy-driven SDEs, SPDEs, and models from biology<br />
<br />
9/30: Benedek<br />
<br />
A very quick introduction to Stein's method. <br />
<br />
I will give a brief introduction to Stein's method, mostly based on the the first couple of sections of the following survey article:<br />
<br />
Ross, N. (2011). Fundamentals of Stein’s method. Probability Surveys, 8, 210-293. <br />
<br />
The following webpage has a huge collection of resources if you want to go deeper: https://sites.google.com/site/yvikswan/about-stein-s-method<br />
<br />
<br />
Note that the Midwest Probability Colloquium (http://www.math.northwestern.edu/mwp/) will have a tutorial program on Stein's method this year. <br />
<br />
10/7, 10/14: Chris J.<br />
[http://www.math.wisc.edu/~janjigia/research/MartingaleProblemNotes.pdf An introduction to the (local) martingale problem.]<br />
<br />
<br />
10/21, 10/28: Dae Han<br />
<br />
11/4, 11/11: Elnur<br />
<br />
11/18, 11/25: Chris N. Free Probability with an emphasis on C* and Von Neumann Algebras<br />
<br />
12/2, 12/9: Yun Zhai<br />
<br />
==2014 Spring==<br />
<br />
<br />
1/28: Greg<br />
<br />
2/04, 2/11: Scott <br />
<br />
[http://www.math.wisc.edu/~shottovy/BLT.pdf Reflected Brownian motion, Occupation time, and applications.] <br />
<br />
2/18: Phil-- Examples of structure results in probability theory.<br />
<br />
2/25, 3/4: Beth-- Derivative estimation for discrete time Markov chains<br />
<br />
3/11, 3/25: Chris J [http://www.math.wisc.edu/~janjigia/research/stationarytalk.pdf Some classical results on stationary distributions of Markov processes]<br />
<br />
4/1, 4/8: Chris N <br />
<br />
4/15, 4/22: Yu Sun<br />
<br />
4/29. 5/6: Diane<br />
<br />
==2013 Fall==<br />
<br />
9/24, 10/1: Chris<br />
[http://www.math.wisc.edu/~janjigia/research/metastabilitytalk.pdf A light introduction to metastability]<br />
<br />
10/8, Dae Han<br />
Majoring multiplicative cascades for directed polymers in random media<br />
<br />
10/15, 10/22: no reading seminar<br />
<br />
10/29, 11/5: Elnur<br />
Limit fluctuations of last passage times <br />
<br />
11/12: Yun<br />
Helffer-Sjostrand representation and Brascamp-Lieb inequality for stochastic interface models<br />
<br />
11/19, 11/26: Yu Sun<br />
<br />
12/3, 12/10: Jason<br />
<br />
==2013 Spring==<br />
<br />
2/13: Elnur <br />
<br />
Young diagrams, RSK correspondence, corner growth models, distribution of last passage times. <br />
<br />
2/20: Elnur<br />
<br />
2/27: Chris<br />
<br />
A brief introduction to enlargement of filtration and the Dufresne identity<br />
[http://www.math.wisc.edu/~janjigia/research/Presentation%20Notes.pdf Notes]<br />
<br />
3/6: Chris<br />
<br />
3/13: Dae Han<br />
<br />
An introduction to random polymers<br />
<br />
3/20: Dae Han<br />
<br />
Directed polymers in a random environment: path localization and strong disorder<br />
<br />
4/3: Diane<br />
<br />
Scale and Speed for honest 1 dimensional diffusions<br />
<br />
References: <br><br />
Rogers & Williams - Diffusions, Markov Processes and Martingales <br><br />
Ito & McKean - Diffusion Processes and their Sample Paths <br><br />
Breiman - Probability <br><br />
http://www.statslab.cam.ac.uk/~beresty/Articles/diffusions.pdf<br />
<br />
4/10: Diane<br />
<br />
4/17: Yun<br />
<br />
Introduction to stochastic interface models<br />
<br />
4/24: Yun<br />
<br />
Dynamics and Gaussian equilibrium sytems<br />
<br />
5/1: This reading seminar will be shifted because of a probability seminar.<br />
<br />
<br />
5/8: Greg, Maso<br />
<br />
The Bethe ansatz vs. The Replica Trick. This lecture is an overview of the two <br />
approaches. See [http://arxiv.org/abs/1212.2267] for a nice overview.<br />
<br />
5/15: Greg, Maso<br />
<br />
Rigorous use of the replica trick.</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Probability&diff=19622Probability2020-09-01T19:34:12Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
= '''Probability at UW-Madison''' =<br />
<br />
<br><br />
<br />
== Tenured and tenure-track faculty ==<br />
<br />
[http://www.math.wisc.edu/~anderson/ David Anderson] (Duke, 2005) applied probability, numerical methods, mathematical biology.<br />
<br />
[http://www.math.wisc.edu/~vadicgor/ Vadim Gorin] (Moscow, 2011) integrable probability, random matrices, asymptotic representation theory<br />
<br />
[http://www.math.wisc.edu/~roch/ Sebastien Roch] (UC Berkeley, 2007) applied probability, mathematical biology, theoretical computer science.<br />
<br />
[http://www.math.wisc.edu/~seppalai/ Timo Seppäläinen] (Minnesota, 1991) motion in a random medium, random growth models, interacting particle systems, large deviation theory.<br />
<br />
[http://www.math.wisc.edu/??? Tatyana Shcherbyna] (Kharkiv, 2012) mathematical physics, random matrices<br />
<br />
[http://www.math.wisc.edu/~hshen3/ Hao Shen] (Princeton, 2013) stochastic partial differential equations, mathematical physics, integrable probability<br />
<br />
[http://www.math.wisc.edu/~valko/ Benedek Valko] (Budapest, 2004) interacting particle systems, random matrices.<br />
<br />
== Emeriti ==<br />
<br />
[http://psoup.math.wisc.edu/kitchen.html David Griffeath] (Cornell, 1976)<br />
<br />
[http://www.math.wisc.edu/~kuelbs Jim Kuelbs] (Minnesota, 1965)<br />
<br />
[http://www.math.wisc.edu/~kurtz Tom Kurtz] (Stanford, 1967)<br />
<br />
Peter Ney (Columbia, 1961)<br />
<br />
Josh Chover (Michigan, 1952)<br />
<br />
<br />
== Postdocs ==<br />
<br />
Erik Bates (Stanford, 2019)<br />
<br />
Scott Smith (Maryland, 2016)<br />
<br />
== Graduate students ==<br />
<br />
<br />
[http://www.math.wisc.edu/~kehlert/ Kurt Ehlert] <br />
<br />
[http://www.math.wisc.edu/~kang Dae Han Kang]<br />
<br />
[https://sites.google.com/a/wisc.edu/brandon-legried/ Brandon Legried]<br />
<br />
Yun Li<br />
<br />
[http://sites.google.com/a/wisc.edu/tung-nguyen/ Tung Nguyen]<br />
<br />
[http://www.math.wisc.edu/~cyuan25/ Chaojie Yuan]<br />
<br />
<br />
<br />
== [[Probability Seminar]] ==<br />
<br />
Thursdays at 2:30pm, VV901<br />
<br />
[https://groups.google.com/a/g-groups.wisc.edu/forum/#!forum/probsem General email list]<br />
<br />
[https://groups.google.com/a/g-groups.wisc.edu/forum/#!forum/lunchwithprobsemspeaker Email list for lunch/dinner with a speaker]<br />
<br />
==[[Graduate student reading seminar]]==<br />
<br />
[https://groups.google.com/a/g-groups.wisc.edu/forum/#!forum/grad_prob_seminar Email list] <br />
<br />
Tuesdays, 2:30pm, 901 Van Vleck<br />
<br />
== [[Probability group timetable]]==<br />
<br />
== [[Undergraduate courses in probability]]==<br />
<br />
== Graduate Courses in Probability ==<br />
<br />
<br />
<br />
'''2020 Fall'''<br />
<br />
Math/Stat 733 Theory of Probability I<br />
<br />
Math/Stat 735 Stochastic Analysis<br />
<br />
Math 833 Topics in Probability: Modern Discrete Probability<br />
<br />
<br />
<br />
'''2021 Spring'''<br />
<br />
Math/Stat 734 Theory of Probability II <br />
<br />
Math 833 Topics in Probability</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Probability_Seminar&diff=19621Probability Seminar2020-09-01T19:27:25Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Fall 2020 =<br />
<br />
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. <br />
<b>We usually end for questions at 3:20 PM.</b><br />
<br />
<b> IMPORTANT: </b> In Fall 2020 the seminar is being run online.<br />
<br />
If you would like to sign up for the email list to receive seminar announcements then please join [https://groups.google.com/a/g-groups.wisc.edu/forum/#!forum/probsem our group].<br />
<br />
== September 15, 2020, [https://www.math.tamu.edu/~bhanin/ Boris Hanin] (Princeton and Texas A&M) ==<br />
<br />
<br />
== September 23, 2020, [https://people.ucd.ie/neil.oconnell Neil O'Connell] (Dublin) ==<br />
<br />
<br />
== October 1, 2020, [https://marcusmichelen.org/ Marcus Michelen], [https://mscs.uic.edu/ UIC] ==<br />
<br />
Title: '''Roots of random polynomials near the unit circle'''<br />
<br />
Abstract: It is a well-known (but perhaps surprising) fact that a polynomial with independent random coefficients has most of its roots very close to the unit circle. Using a probabilistic perspective, we understand the behavior of roots of random polynomials exceptionally close to the unit circle and prove several limit theorems; these results resolve several conjectures of Shepp and Vanderbei. We will also discuss how our techniques provide a heuristic, probabilistic explanation for why random polynomials tend to have most roots near the unit circle. Based on joint work with Julian Sahasrabudhe.<br />
<br />
== October 8, 2020, [http://sites.harvard.edu/~sus977/index.html Subhabrata Sen], [https://statistics.fas.harvard.edu/ Harvard] ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
== November 12, 2020, [http://stanford.edu/~ajdunl2/ Alexander Dunlap], [https://cims.nyu.edu/ NYU Courant Institute] ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
<br />
[[Past Seminars]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19603Colloquia2020-08-31T19:33:34Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2020=<br />
<br />
== September 25, 2020, [https://www.math.tamu.edu/~jml/ Joseph Landsberg] (Texas A&M) ==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
== October 9, 2020, TBA ==<br />
<br />
== October 23, 2020, TBA ==<br />
<br />
== November 6, 2020, [http://math.jhu.edu/~sakellar/ Yiannis Sakellaridis] (Johns Hopkins University)==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
== November 20, 2020, TBA ==<br />
<br />
== December 4, 2020, TBA ==<br />
<br />
<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19602Colloquia2020-08-31T19:33:03Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2020=<br />
<br />
== September 25, 2020, [https://www.math.tamu.edu/~jml/ Joseph Landsberg] (Texas A&M) ==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
== October 9, 2020, TBA ==<br />
<br />
== October 23, 2020, TBA ==<br />
<br />
== November 6, 2020, [http://math.jhu.edu/~sakellar/ Yiannis Sakellaridis] (Johns Hopkins University)==<br />
<br />
== November 20, 2020, TBA ==<br />
<br />
== December 4, 2020, TBA ==<br />
<br />
<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Probability_Seminar&diff=19598Probability Seminar2020-08-31T16:28:11Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Fall 2020 =<br />
<br />
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. <br />
<b>We usually end for questions at 3:20 PM.</b><br />
<br />
<b> IMPORTANT: </b> In Fall 2020 the seminar is being run online.<br />
<br />
If you would like to sign up for the email list to receive seminar announcements then please send an email to <br />
[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]<br />
<br />
<br />
== September 15, 2020, [https://www.math.tamu.edu/~bhanin/ Boris Hanin] (Princeton and Texas A&M) ==<br />
<br />
<br />
== September 23, 2020, [https://people.ucd.ie/neil.oconnell Neil O'Connell] (Dublin) ==<br />
<br />
<br />
== October 1, 2020, [https://marcusmichelen.org/ Marcus Michelen], [https://mscs.uic.edu/ UIC] ==<br />
<br />
Title: '''Roots of random polynomials near the unit circle'''<br />
<br />
Abstract: It is a well-known (but perhaps surprising) fact that a polynomial with independent random coefficients has most of its roots very close to the unit circle. Using a probabilistic perspective, we understand the behavior of roots of random polynomials exceptionally close to the unit circle and prove several limit theorems; these results resolve several conjectures of Shepp and Vanderbei. We will also discuss how our techniques provide a heuristic, probabilistic explanation for why random polynomials tend to have most roots near the unit circle. Based on joint work with Julian Sahasrabudhe.<br />
<br />
<br />
[[Past Seminars]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Probability_Seminar&diff=19597Probability Seminar2020-08-31T16:26:43Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Fall 2020 =<br />
<br />
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. <br />
<b>We usually end for questions at 3:20 PM.</b><br />
<br />
<b> IMPORTANT: </b> In Fall 2020 the seminar is being run online.<br />
<br />
If you would like to sign up for the email list to receive seminar announcements then please send an email to <br />
[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]<br />
<br />
<br />
== September 15, 2020, [https://www.math.tamu.edu/~bhanin/ Boris Hanin] (Princeton and Texas A&M) ==<br />
'''TBA<br />
'''<br />
<br />
<br />
== September 23, 2020, ==<br />
<br />
<br />
== October 1, 2020, [https://marcusmichelen.org/ Marcus Michelen], [https://mscs.uic.edu/ UIC] ==<br />
<br />
Title: '''Roots of random polynomials near the unit circle'''<br />
<br />
Abstract: It is a well-known (but perhaps surprising) fact that a polynomial with independent random coefficients has most of its roots very close to the unit circle. Using a probabilistic perspective, we understand the behavior of roots of random polynomials exceptionally close to the unit circle and prove several limit theorems; these results resolve several conjectures of Shepp and Vanderbei. We will also discuss how our techniques provide a heuristic, probabilistic explanation for why random polynomials tend to have most roots near the unit circle. Based on joint work with Julian Sahasrabudhe.<br />
<br />
<br />
[[Past Seminars]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19595Colloquia2020-08-31T14:19:29Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2020=<br />
<br />
== September 25, 2020, [https://www.math.tamu.edu/~jml/ Joseph Landsberg] (Texas A&M) ==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
== October 9, 2020, TBA ==<br />
<br />
== October 23, 2020, TBA ==<br />
<br />
== November 6, 2020, TBA ==<br />
<br />
== November 20, 2020, TBA ==<br />
<br />
== December 4, 2020, TBA ==<br />
<br />
<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19592Colloquia2020-08-29T19:25:50Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2020=<br />
<br />
== September 18, 2020, TBA ==<br />
<br />
== September 25, 2020, [https://www.math.tamu.edu/~jml/ Joseph Landsberg] (Texas A&M) ==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
== October 2, 2020, TBA ==<br />
<br />
== October 9, 2020, TBA ==<br />
<br />
== October 16, 2020, TBA ==<br />
<br />
== October 23, 2020, TBA ==<br />
<br />
== October 30, 2020, TBA ==<br />
<br />
<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19591Colloquia2020-08-29T19:25:33Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2020=<br />
<br />
== September 18, 2020, TBA ==<br />
<br />
<br />
== September 25, 2020, [https://www.math.tamu.edu/~jml/ Joseph Landsberg] (Texas A&M) ==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
<br />
== October 2, 2020, TBA ==<br />
<br />
== October 9, 2020, TBA ==<br />
<br />
== October 16, 2020, TBA ==<br />
<br />
== October 23, 2020, TBA ==<br />
<br />
== October 30, 2020, TBA ==<br />
<br />
<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19590Colloquia2020-08-29T19:24:41Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2020=<br />
<br />
== September 18, 2020, [TBA} ==<br />
<br />
<br />
== September 25, 2020, [https://www.math.tamu.edu/~jml/ Joseph Landsberg] (Texas A&M) ==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
<br />
== October 2, 2020, [TBA] (TBA) ==<br />
<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19566Colloquia2020-08-23T21:10:44Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2020=<br />
<br />
== September 18, 2020, ==<br />
<br />
<br />
== September 25, 2020, [https://www.math.tamu.edu/~jml/ Joseph Landsberg] (Texas A&M) ==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19564Colloquia2020-08-19T18:10:55Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2020=<br />
<br />
== September 18, 2020, [https://users.oden.utexas.edu/~pgm/ Per-Gunnar Martinsson] (UT-Austin) ==<br />
<br />
(Hosted by Li)<br />
<br />
<br />
== September 25, 2020, [https://www.math.tamu.edu/~jml/ Joseph Landsberg] (Texas A&M) ==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall_2020&diff=19554Colloquia/Fall 20202020-08-15T02:30:27Z<p>Vadicgor: Blanked the page</p>
<hr />
<div></div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19553Colloquia2020-08-15T02:29:23Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2020=<br />
<br />
== September 18, 2020, [https://users.oden.utexas.edu/~pgm/ Per-Gunnar Martinsson] (UT-Austin) ==<br />
<br />
(Hosted by Li)<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
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[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19552Colloquia2020-08-15T02:29:08Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
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<b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
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<br />
=Fall 2020=<br />
<br />
== September 18, 2020, [https://users.oden.utexas.edu/~pgm/ Per-Gunnar Martinsson] (UT-Austin) ==<br />
<br />
(Hosted by Li)<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
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[[Colloquia/Spring2019|Spring 2019]]<br />
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[[Colloquia/Fall2018|Fall 2018]]<br />
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[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19551Colloquia2020-08-15T02:28:51Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b> Mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
<br />
<br />
=Fall 2020=<br />
<br />
== September 18, 2020, [https://users.oden.utexas.edu/~pgm/ Per-Gunnar Martinsson] (UT-Austin) ==<br />
<br />
(Hosted by Li)<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
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[[Colloquia/Spring2019|Spring 2019]]<br />
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[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19550Colloquia2020-08-15T02:28:08Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
Mathematics Colloquium is ONLINE on Fridays at 4:00 pm <br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
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<br />
<br />
=Fall 2020=<br />
<br />
== September 18, 2020, [https://users.oden.utexas.edu/~pgm/ Per-Gunnar Martinsson] (UT-Austin) ==<br />
<br />
(Hosted by Li)<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
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[[Colloquia/Spring2019|Spring 2019]]<br />
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[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19549Colloquia2020-08-15T02:26:46Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
Mathematics Colloquium is ONLINE on Fridays at 4:00 pm <br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
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<br />
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=Fall 2020=<br />
<br />
== September 18, 2020, [https://www.math.wisc.edu/ Our speaker] (UW Madison) ==<br />
<br />
'''Title<br />
'''<br />
<br />
Abstract<br />
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<br />
== Past Colloquia ==<br />
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[[Colloquia/Spring2020|Spring 2020]]<br />
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[[Colloquia/Fall2019|Fall 2019]]<br />
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[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19548Colloquia2020-08-15T02:26:09Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are ONLINE on Fridays at 4:00 pm <br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
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<br />
<br />
==Fall 2020==<br />
<br />
== September 18, 2020, [https://www.math.wisc.edu/ Our speaker] (UW Madison) ==<br />
<br />
'''Title<br />
'''<br />
<br />
Abstract<br />
<br />
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== Past Colloquia ==<br />
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[[Colloquia/Spring2020|Spring 2020]]<br />
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[[Colloquia/Fall2019|Fall 2019]]<br />
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[[Colloquia/Spring2019|Spring 2019]]<br />
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[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19547Colloquia2020-08-15T02:22:19Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are ONLINE on Fridays at 4:00 pm <br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
<br />
<br />
==Fall 2020==<br />
<br />
<br />
<br />
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== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
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[[Colloquia/Fall2019|Fall 2019]]<br />
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[[Colloquia/Spring2019|Spring 2019]]<br />
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[[WIMAW]]<br />
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<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 18<br />
| [https://users.oden.utexas.edu/~pgm/ Per-Gunnar Martinsson] (UT-Austin)<br />
| [[#Per-Gunnar Martinsson (UT-Austin) | TBA ]]<br />
| Li<br />
|-<br />
|Sept 25<br />
| [webpage name] (institute)<br />
|[[#name (institute)| Title ]]<br />
| host</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19546Colloquia2020-08-15T02:21:19Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are ONLINE on Fridays at 4:00 pm <br />
<br />
%in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2020==<br />
<br />
<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
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[[Colloquia/Fall2018|Fall 2018]]<br />
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[[Colloquia/Fall2017|Fall 2017]]<br />
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[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
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[[Colloquia/Spring2016|Spring 2016]]<br />
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[[Colloquia/Fall2015|Fall 2015]]<br />
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[[Colloquia/Spring2014|Spring 2015]]<br />
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[[Colloquia/Spring2014|Spring 2014]]<br />
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[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 18<br />
| [https://users.oden.utexas.edu/~pgm/ Per-Gunnar Martinsson] (UT-Austin)<br />
| [[#Per-Gunnar Martinsson (UT-Austin) | TBA ]]<br />
| Li<br />
|-<br />
|Sept 25<br />
| [webpage name] (institute)<br />
|[[#name (institute)| Title ]]<br />
| host</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19545Colloquia2020-08-15T02:13:10Z<p>Vadicgor: </p>
<hr />
<div>{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 18<br />
| [https://users.oden.utexas.edu/~pgm/ Per-Gunnar Martinsson] (UT-Austin)<br />
| [[#Per-Gunnar Martinsson (UT-Austin) | TBA ]]<br />
| Li<br />
|-<br />
|Sept 25<br />
| [webpage name] (institute)<br />
|[[#name (institute)| Title ]]<br />
| host</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2020&diff=19543Colloquia/Spring20202020-08-15T02:11:33Z<p>Vadicgor: Vadicgor moved page Colloquia to Colloquia/Spring2020</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 10<br />
|Thomas Lam (Michigan) <br />
|[[#Thomas Lam (Michigan) |Positive geometries and string theory amplitudes]]<br />
|Erman<br />
|-<br />
|Jan 21 '''Tuesday 4-5 pm in B139'''<br />
|[http://www.nd.edu/~cholak/ Peter Cholak] (Notre Dame) <br />
|[[#Peter Cholak (Notre Dame) |What can we compute from solutions to combinatorial problems?]]<br />
|Lempp<br />
|-<br />
|Jan 24<br />
|[https://math.duke.edu/people/saulo-orizaga Saulo Orizaga] (Duke)<br />
|[[#Saulo Orizaga (Duke) | Introduction to phase field models and their efficient numerical implementation ]]<br />
|<br />
|-<br />
|Jan 27 '''Monday 4-5 pm in 911'''<br />
|[https://math.yale.edu/people/caglar-uyanik Caglar Uyanik] (Yale)<br />
|[[#Caglar Uyanik (Yale) | Hausdorff dimension and gap distribution in billiards ]]<br />
|Ellenberg<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|[[#Andy Zucker (Lyon) |Topological dynamics of countable groups and structures]]<br />
|Soskova/Lempp<br />
|-<br />
|Jan 31 <br />
|[https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke)<br />
|[[#Lillian Pierce (Duke) |On Bourgain’s counterexample for the Schrödinger maximal function]]<br />
|Marshall/Seeger<br />
|-<br />
|Feb 7<br />
|[https://web.math.princeton.edu/~jkileel/ Joe Kileel] (Princeton)<br />
|[[#Joe Kileel (Princeton) |Inverse Problems, Imaging and Tensor Decomposition]]<br />
|Roch<br />
|-<br />
|Feb 10<br />
|[https://clvinzan.math.ncsu.edu/ Cynthia Vinzant] (NCSU)<br />
|[[#Cynthia Vinzant (NCSU) |Matroids, log-concavity, and expanders]]<br />
|Roch/Erman<br />
|-<br />
|Feb 12 '''Wednesday 4-5 pm in VV 911'''<br />
|[https://www.machuang.org/ Jinzi Mac Huang] (UCSD)<br />
|[[#Jinzi Mac Huang (UCSD) |Mass transfer through fluid-structure interactions]]<br />
|Spagnolie<br />
|-<br />
|Feb 14<br />
|[https://math.unt.edu/people/william-chan/ William Chan] (University of North Texas)<br />
|[[#William Chan (University of North Texas) |Definable infinitary combinatorics under determinacy]]<br />
|Soskova/Lempp<br />
|-<br />
|Feb 17<br />
|[https://yisun.io/ Yi Sun] (Columbia)<br />
|[[#Yi Sun (Columbia) |Fluctuations for products of random matrices]]<br />
|Roch<br />
|-<br />
|Feb 19<br />
|[https://www.math.upenn.edu/~zwang423// Zhenfu Wang] (University of Pennsylvania)<br />
|[[#Zhenfu Wang (University of Pennsylvania) |Quantitative Methods for the Mean Field Limit Problem]]<br />
|Tran<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|[[#Shai Evra (IAS) |Golden Gates in PU(n) and the Density Hypothesis]]<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|[[#Brett Wick (WUSTL) |The Corona Theorem]]<br />
|Seeger<br />
|-<br />
|March 6 '''in 911'''<br />
| Jessica Fintzen (Michigan)<br />
|[[#Jessica Fintzen (Michigan) | Representations of p-adic groups]]<br />
|Marshall<br />
|-<br />
|March 13 '''CANCELLED'''<br />
| [https://plantpath.wisc.edu/claudia-solis-lemus// Claudia Solis Lemus] (UW-Madison, Plant Pathology)<br />
|[[#Claudia Solis Lemus | New challenges in phylogenetic inference]]<br />
|Anderson<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27 '''CANCELLED'''<br />
|[https://max.lieblich.us/ Max Lieblich] (Univ. of Washington, Seattle)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3 '''CANCELLED'''<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| No colloquium<br />
|<br />
| <br />
|-<br />
|April 17<br />
|JM Landsberg (TAMU)<br />
|TBA<br />
|Gurevich<br />
|-<br />
|April 23<br />
|Martin Hairer (Imperial College London)<br />
|Wolfgang Wasow Lecture<br />
|Hao Shen<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Thomas Lam (Michigan) === <br />
<br />
Title: Positive geometries and string theory amplitudes<br />
<br />
Abstract: Inspired by developments in quantum field theory, we<br />
recently defined the notion of a positive geometry, a class of spaces<br />
that includes convex polytopes, positive parts of projective toric<br />
varieties, and positive parts of flag varieties. I will discuss some<br />
basic features of the theory and an application to genus zero string<br />
theory amplitudes. As a special case, we obtain the Euler beta<br />
function, familiar to mathematicians, as the "stringy canonical form"<br />
of the closed interval.<br />
<br />
This talk is based on joint work with Arkani-Hamed, Bai, and He.<br />
<br />
=== Peter Cholak (Notre Dame) ===<br />
<br />
Title: What can we compute from solutions to combinatorial problems?<br />
<br />
Abstract: This will be an introductory talk to an exciting current <br />
research area in mathematical logic. Mostly we are interested in <br />
solutions to Ramsey's Theorem. Ramsey's Theorem says for colorings <br />
C of pairs of natural numbers, there is an infinite set H such that <br />
all pairs from H have the same constant color. H is called a homogeneous <br />
set for C. What can we compute from H? If you are not sure, come to <br />
the talk and find out!<br />
<br />
=== Saulo Orizaga (Duke) ===<br />
<br />
Title: Introduction to phase field models and their efficient numerical implementation<br />
<br />
Abstract: In this talk we will provide an introduction to phase field models. We will focus in models<br />
related to the Cahn-Hilliard (CH) type of partial differential equation (PDE). We will discuss the<br />
challenges associated in solving such higher order parabolic problems. We will present several<br />
new numerical methods that are fast and efficient for solving CH or CH-extended type of problems.<br />
The new methods and their energy-stability properties will be discussed and tested with several computational examples commonly found in material science problems. If time allows, we will talk about more applications in which phase field models are useful and applicable.<br />
<br />
=== Caglar Uyanik (Yale) ===<br />
<br />
Title: Hausdorff dimension and gap distribution in billiards<br />
<br />
Abstract: A classical “unfolding” procedure allows one to turn questions about billiard trajectories in a Euclidean polygon into questions about the geodesic flow on a surface equipped with a certain geometric structure. Surprisingly, the flow on the surface is in turn related to the geodesic flow on the classical moduli spaces of Riemann surfaces. Building on recent breakthrough results of Eskin-Mirzakhani-Mohammadi, we prove a large deviations result for Birkhoff averages as well as generalize a classical theorem of Masur on geodesics in the moduli spaces of translation surfaces. <br />
<br />
=== Andy Zucker (Lyon) ===<br />
<br />
Title: Topological dynamics of countable groups and structures<br />
<br />
Abstract: We give an introduction to the abstract topological dynamics <br />
of topological groups, i.e. the study of the continuous actions of a <br />
topological group on a compact space. We are particularly interested <br />
in the minimal actions, those for which every orbit is dense. <br />
The study of minimal actions is aided by a classical theorem of Ellis, <br />
who proved that for any topological group G, there exists a universal <br />
minimal flow (UMF), a minimal G-action which factors onto every other <br />
minimal G-action. Here, we will focus on two classes of groups: <br />
a countable discrete group and the automorphism group of a countable <br />
first-order structure. In the case of a countable discrete group, <br />
Baire category methods can be used to show that the collection of <br />
minimal flows is quite rich and that the UMF is rather complicated. <br />
For an automorphism group G of a countable structure, combinatorial <br />
methods can be used to show that sometimes, the UMF is trivial, or <br />
equivalently that every continuous action of G on a compact space <br />
admits a global fixed point.<br />
<br />
=== Lillian Pierce (Duke) ===<br />
<br />
Title: On Bourgain’s counterexample for the Schrödinger maximal function<br />
<br />
Abstract: In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space $H^s$ must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
=== Joe Kileel (Princeton) ===<br />
<br />
Title: Inverse Problems, Imaging and Tensor Decomposition<br />
<br />
Abstract: Perspectives from computational algebra and optimization are brought <br />
to bear on a scientific application and a data science application. <br />
In the first part of the talk, I will discuss cryo-electron microscopy <br />
(cryo-EM), an imaging technique to determine the 3-D shape of <br />
macromolecules from many noisy 2-D projections, recognized by the 2017 <br />
Chemistry Nobel Prize. Mathematically, cryo-EM presents a <br />
particularly rich inverse problem, with unknown orientations, extreme <br />
noise, big data and conformational heterogeneity. In particular, this <br />
motivates a general framework for statistical estimation under compact <br />
group actions, connecting information theory and group invariant <br />
theory. In the second part of the talk, I will discuss tensor rank <br />
decomposition, a higher-order variant of PCA broadly applicable in <br />
data science. A fast algorithm is introduced and analyzed, combining <br />
ideas of Sylvester and the power method.<br />
<br />
=== Cynthia Vinzant (NCSU) ===<br />
<br />
Title: Matroids, log-concavity, and expanders<br />
<br />
Abstract: Matroids are combinatorial objects that model various types of independence. They appear several fields mathematics, including graph theory, combinatorial optimization, and algebraic geometry. In this talk, I will introduce the theory of matroids along with the closely related class of polynomials called strongly log-concave polynomials. Strong log-concavity is a functional property of a real multivariate polynomial that translates to useful conditions on its coefficients. Discrete probability distributions defined by these coefficients inherit several of these nice properties. I will discuss the beautiful real and combinatorial geometry underlying these polynomials and describe applications to random walks on the faces of simplicial complexes. Consequences include proofs of Mason's conjecture that the sequence of numbers of independent sets of a matroid is ultra log-concave and the Mihail-Vazirani conjecture that the basis exchange graph of a matroid has expansion at least one. This is based on joint work with Nima Anari, Kuikui Liu, and Shayan Oveis Gharan.<br />
<br />
=== Jinzi Mac Huang (UCSD) ===<br />
<br />
Title: Mass transfer through fluid-structure interactions<br />
<br />
Abstract: The advancement of mathematics is closely associated with new discoveries from physical experiments. On one hand, mathematical tools like numerical simulation can help explain observations from experiments. On the other hand, experimental discoveries of physical phenomena, such as Brownian motion, can inspire the development of new mathematical approaches. In this talk, we focus on the interplay between applied math and experiments involving fluid-structure interactions -- a fascinating topic with both physical relevance and mathematical complexity. One such problem, inspired by geophysical fluid dynamics, is the experimental and numerical study of the dissolution of solid bodies in a fluid flow. The results of this study allow us to sketch mathematical answers to some long standing questions like the formation of stone forests in China and Madagascar, and how many licks it takes to get to the center of a Tootsie Pop. We will also talk about experimental math problems at the micro-scale, focusing on the mass transport process of diffusiophoresis, where colloidal particles are advected by a concentration gradient of salt solution. Exploiting this phenomenon, we see that colloids are able to navigate a micro-maze that has a salt concentration gradient across the exit and entry points. We further demonstrate that their ability to solve the maze is closely associated with the properties of a harmonic function – the salt concentration.<br />
<br />
=== William Chan (University of North Texas) ===<br />
<br />
Title: Definable infinitary combinatorics under determinacy<br />
<br />
Abstract: The axiom of determinacy, AD, states that in any infinite two player integer game of a certain form, one of the two players must have a winning strategy. It is incompatible with the ZFC set theory axioms with choice; however, it is a succinct extension of ZF which implies many subsets of the real line possess familiar regularity properties and eliminates many pathological sets. For instance, AD implies all sets of reals are Lebesgue measurable and every function from the reals to the reals is continuous on a comeager set. Determinacy also implies that the first uncountable cardinal has the strong partition property which can be used to define the partition measures. This talk will give an overview of the axiom of determinacy and will discuss recent results on the infinitary combinatorics surrounding the first uncountable cardinal and its partition measures. I will discuss the almost everywhere continuity phenomenon for functions outputting countable ordinals and the almost-everywhere uniformization results for closed and unbounded subsets of the first uncountable cardinal. These will be used to describe the rich structure of the cardinals below the powerset of the first and second uncountable cardinals under determinacy assumptions and to investigate the ultrapowers by these partition measures.<br />
<br />
=== Yi Sun (Columbia) ===<br />
<br />
Title: Fluctuations for products of random matrices<br />
<br />
Abstract: Products of large random matrices appear in many modern applications such as high dimensional statistics (MANOVA estimators), machine learning (Jacobians of neural networks), and population ecology (transition matrices of dynamical systems). Inspired by these situations, this talk concerns global limits and fluctuations of singular values of products of independent random matrices as both the size N and number M of matrices grow. As N grows, I will show for a variety of ensembles that fluctuations of the Lyapunov exponents converge to explicit Gaussian fields which transition from log-correlated for fixed M to having a white noise component for M growing with N. I will sketch our method, which uses multivariate generalizations of the Laplace transform based on the multivariate Bessel function from representation theory.<br />
<br />
=== Zhenfu Wang (University of Pennsylvania) ===<br />
<br />
Title: Quantitative Methods for the Mean Field Limit Problem<br />
<br />
Abstract: We study the mean field limit of large systems of interacting particles. Classical mean field limit results require that the interaction kernels be essentially Lipschitz. To handle more singular interaction kernels is a longstanding and challenging question but which now has some successes. Joint with P.-E. Jabin, we use the relative entropy between the joint law of all particles and the tensorized law at the limit to quantify the convergence from the particle systems towards the macroscopic PDEs. This method requires to prove large deviations estimates for non-continuous potentials modified by the limiting law. But it leads to explicit convergence rates for all marginals. This in particular can be applied to the Biot-Savart law for 2D Navier-Stokes. To treat more general and singular kernels, joint with D. Bresch and P.-E. Jabin, we introduce the modulated free energy, combination of the relative entropy that we had previously developed and of the modulated energy introduced by S. Serfaty. This modulated free energy may be understood as introducing appropriate weights in the relative entropy to cancel the most singular terms involving the divergence of the kernels. Our modulated free energy allows to treat gradient flows with singular potentials which combine large smooth part, small attractive singular part and large repulsive singular part. As an example, a full rigorous derivation (with quantitative estimates) of some chemotaxis models, such as the Patlak-Keller-Segel system in the subcritical regimes, is obtained.<br />
<br />
===Shai Evra (IAS)===<br />
<br />
Title: Golden Gates in PU(n) and the Density Hypothesis.<br />
<br />
Abstract: In their seminal work from the 80’s, Lubotzky, Phillips and Sarnak gave explicit constructions of topological generators for PU(2) with optimal covering properties. In this talk I will describe some recent works that extend the construction of LPS to higher rank compact Lie groups. <br />
<br />
A key ingredient in the work of LPS is the Ramanujan conjecture for U(2), which follows from Deligne's proof of the Ramanujan-Petersson conjecture for GL(2). Unfortunately, the naive generalization of the Ramanujan conjecture is false for higher rank groups. Following a program initiated by Sarnak in the 90's, we prove a density hypothesis and use it as a replacement of the naive Ramanujan conjecture.<br />
<br />
This talk is based on some joint works with Ori Parzanchevski and Amitay Kamber.<br />
<br />
<br />
===Brett Wick (WUSTL)===<br />
<br />
Title: The Corona Theorem<br />
<br />
Abstract: Carleson's Corona Theorem has served as a major motivation for many results in complex function theory, operator theory and harmonic analysis. In a simple form, the result states that for $N$ bounded analytic functions $f_1,\ldots,f_N$ on the unit disc such that $\inf \left\vert f_1\right\vert+\cdots+\left\vert f_N\right\vert\geq\delta>0$ it is possible to find $N$ other bounded analytic functions $g_1,\ldots,g_N$ such that $f_1g_1+\cdots+f_Ng_N =1$. Moreover, the functions $g_1,\ldots,g_N$ can be chosen with some norm control.<br />
<br />
In this talk we will discuss some generalizations of this result to certain vector valued functions and connections with geometry and to function spaces on the unit ball in several complex variables.<br />
<br />
===Claudia Solis Lemus===<br />
<br />
Title New challenges in phylogenetic inference<br />
<br />
Abstract: Phylogenetics studies the evolutionary relationships between different organisms, and its main goal is the inference of the Tree of Life. Usual statistical inference techniques like maximum likelihood and bayesian inference through Markov chain Monte Carlo (MCMC) have been widely used, but their performance deteriorates as the datasets increase in number of genes or number of species. I will present different approaches to improve the scalability of phylogenetic inference: from divide-and-conquer methods based on pseudolikelihood, to computation of Frechet means in BHV space, finally concluding with neural network models to approximate posterior distributions in tree space. The proposed methods will allow scientists to include more species into the Tree of Life, and thus complete a broader picture of evolution.<br />
<br />
===Jessica Fintzen (Michigan)===<br />
<br />
Title: Representations of p-adic groups<br />
<br />
Abstract: The Langlands program is a far-reaching collection of conjectures that relate different areas of mathematics including number theory and representation theory. A fundamental problem on the representation theory side of the Langlands program is the construction of all (irreducible, smooth, complex) representations of certain matrix groups, called p-adic groups.<br />
In my talk I will introduce p-adic groups and provide an overview of our understanding of their representations, with an emphasis on recent progress. I will also briefly discuss applications to other areas, e.g. to automorphic forms and the global Langlands program.<br />
<br />
<br />
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[[WIMAW]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=19544Colloquia2020-08-15T02:11:33Z<p>Vadicgor: Vadicgor moved page Colloquia to Colloquia/Spring2020</p>
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<div>#REDIRECT [[Colloquia/Spring2020]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Probability_Seminar&diff=19539Probability Seminar2020-08-12T22:28:50Z<p>Vadicgor: </p>
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<div>__NOTOC__<br />
<br />
= Fall 2020 =<br />
<br />
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. <br />
<b>We usually end for questions at 3:20 PM.</b><br />
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<b> IMPORTANT: </b> In Fall 2020 the seminar is being run online.<br />
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== September 3, 2020, [https://math.wisc.edu TBA] (TBA) ==<br />
'''TBA<br />
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== September 10, 2020, ==<br />
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[[Past Seminars]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Past_Seminars&diff=19538Past Seminars2020-08-12T22:20:54Z<p>Vadicgor: </p>
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<!-- [http://www.math.wisc.edu/~probsem/list-old-sem.html Webpage for older past probability seminars] --></div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Probability_Seminar&diff=19537Probability Seminar2020-08-12T22:20:27Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Spring 2020 =<br />
<br />
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. <br />
<b>We usually end for questions at 3:20 PM.</b><br />
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If you would like to sign up for the email list to receive seminar announcements then please send an email to <br />
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== September 3, 2020, [https://math.wisc.edu TBA] (TBA) ==<br />
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== September 10, 2020, ==<br />
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[[Past Seminars]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Talk:Past_Probability_Seminars_Spring_2020&diff=19535Talk:Past Probability Seminars Spring 20202020-08-12T22:18:20Z<p>Vadicgor: Vadicgor moved page Talk:Probability Seminar to Talk:Past Probability Seminars Spring 2020</p>
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<div></div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Probability_Seminar&diff=19534Probability Seminar2020-08-12T22:18:20Z<p>Vadicgor: Vadicgor moved page Probability Seminar to Past Probability Seminars Spring 2020</p>
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<div>#REDIRECT [[Past Probability Seminars Spring 2020]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Talk:Probability_Seminar&diff=19536Talk:Probability Seminar2020-08-12T22:18:20Z<p>Vadicgor: Vadicgor moved page Talk:Probability Seminar to Talk:Past Probability Seminars Spring 2020</p>
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<div>#REDIRECT [[Talk:Past Probability Seminars Spring 2020]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Past_Probability_Seminars_Spring_2020&diff=19533Past Probability Seminars Spring 20202020-08-12T22:18:19Z<p>Vadicgor: Vadicgor moved page Probability Seminar to Past Probability Seminars Spring 2020</p>
<hr />
<div>__NOTOC__<br />
<br />
= Spring 2020 =<br />
<br />
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. <br />
<b>We usually end for questions at 3:20 PM.</b><br />
<br />
If you would like to sign up for the email list to receive seminar announcements then please send an email to <br />
[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]<br />
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== January 23, 2020, [https://www.math.wisc.edu/~seppalai/ Timo Seppalainen] (UW Madison) ==<br />
'''Non-existence of bi-infinite geodesics in the exponential corner growth model<br />
'''<br />
<br />
Whether bi-infinite geodesics exist has been a significant open problem in first- and last-passage percolation since the mid-80s. A non-existence proof in the case of directed planar last-passage percolation with exponential weights was posted by Basu, Hoffman and Sly in November 2018. Their proof utilizes estimates from integrable probability. This talk describes an independent proof completed 10 months later that relies on couplings, coarse graining, and control of geodesics through planarity and increment-stationary last-passage percolation. Joint work with Marton Balazs and Ofer Busani (Bristol).<br />
<br />
== January 30, 2020, [https://www.math.wisc.edu/people/vv-prof-directory Scott Smith] (UW Madison) ==<br />
'''Quasi-linear parabolic equations with singular forcing'''<br />
<br />
The classical solution theory for stochastic ODE's is centered around Ito's stochastic integral. By intertwining ideas from analysis and probability, this approach extends to many PDE's, a canonical example being multiplicative stochastic heat equations driven by space-time white noise. In both the ODE and PDE settings, the solution theory is beyond the scope of classical deterministic theory because of the ambiguity in multiplying a function with a white noise. The theory of rough paths and regularity structures provides a more quantitative understanding of this difficulty, leading to a more refined solution theory which efficiently divides the analytic and probabilistic aspects of the problem, and remarkably, even has an algebraic component.<br />
<br />
In this talk, we will discuss a new application of these ideas to stochastic heat equations where the strength of the diffusion is not constant but random, as it depends locally on the solution. These are known as quasi-linear equations. Our main result yields the deterministic side of a solution theory for these PDE's, modulo a suitable renormalization. Along the way, we identify a formally infinite series expansion of the solution which guides our analysis, reveals a nice algebraic structure, and encodes the counter-terms in the PDE. This is joint work with Felix Otto, Jonas Sauer, and Hendrik Weber.<br />
<br />
== February 6, 2020, [https://sites.google.com/site/cyleeken/ Cheuk-Yin Lee] (Michigan State) ==<br />
'''Sample path properties of stochastic partial differential equations: modulus of continuity and multiple points'''<br />
<br />
In this talk, we will discuss sample path properties of stochastic partial differential equations (SPDEs). We will present a sharp regularity result for the stochastic wave equation driven by an additive Gaussian noise that is white in time and colored in space. We prove the exact modulus of continuity via the property of local nondeterminism. We will also discuss the existence problem for multiple points (or self-intersections) of the sample paths of SPDEs. Our result shows that multiple points do not exist in the critical dimension for a large class of Gaussian random fields including the solution of a linear system of stochastic heat or wave equations.<br />
<br />
== February 13, 2020, [http://www.jelena-diakonikolas.com/ Jelena Diakonikolas] (UW Madison) ==<br />
'''Langevin Monte Carlo Without Smoothness'''<br />
<br />
Langevin Monte Carlo (LMC) is an iterative algorithm used to generate samples from a distribution that is known only up to a normalizing constant. The nonasymptotic dependence of its mixing time on the dimension and target accuracy is understood mainly in the setting of smooth (gradient-Lipschitz) log-densities, a serious limitation for applications in machine learning. We remove this limitation by providing polynomial-time convergence guarantees for a variant of LMC in the setting of non-smooth log-concave distributions. At a high level, our results follow by leveraging the implicit smoothing of the log-density that comes from a small Gaussian perturbation that we add to the iterates of the algorithm and while controlling the bias and variance that are induced by this perturbation.<br />
Based on joint work with Niladri Chatterji, Michael I. Jordan, and Peter L. Bartlett.<br />
<br />
== February 20, 2020, [https://math.berkeley.edu/~pmwood/ Philip Matchett Wood] (UC Berkeley) ==<br />
'''A replacement principle for perturbations of non-normal matrices'''<br />
<br />
There are certain non-normal matrices whose eigenvalues can change dramatically when a small perturbation is added. However, when that perturbation is an iid random matrix, it appears that the eigenvalues become stable after perturbation and only change slightly when further small perturbations are added. Much of the work is this situation has focused on iid random gaussian perturbations. In this talk, we will discuss work on a universality result that allows for consideration of non-gaussian perturbations, and that shows that all perturbations satisfying certain conditions will produce the same limiting eigenvalue measure. Interestingly, this even allows for deterministic perturbations to be considered. Joint work with Sean O'Rourke.<br />
<br />
== February 27, 2020, No seminar ==<br />
''' '''<br />
<br />
== March 5, 2020, [https://www.ias.edu/scholars/jiaoyang-huang Jiaoyang Huang] (IAS) ==<br />
''' Large Deviation Principles via Spherical Integrals'''<br />
<br />
In this talk, I'll explain a framework to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the asymptotics of spherical integrals obtained by Guionnet and Zeitouni. As examples, we obtain <br />
<br />
1) the large deviation principle for the empirical distribution of the diagonal entries of $UB_NU^*$, for a sequence of $N\times N$ diagonal matrices $B_N$ and unitary/orthogonal Haar distributed matrices $U$;<br />
<br />
2) the large deviation upper bound for the empirical eigenvalue distribution of $A_N+UB_NU^*$, for two sequences of $N\times N$ diagonal matrices $A_N, B_N$, and their complementary lower bounds at "good" probability distributions;<br />
<br />
3) the large deviation principle for the Kostka number $K_{\lambda_N \eta_N}$, for two sequences of partitions $\lambda_N, \eta_N$ with at most $N$ rows;<br />
<br />
4) the large deviation upper bound for the Littlewood-Richardson coefficients $c_{\lambda_N \eta_N}^{\kappa_N}$, for three sequences of partitions $\lambda_N, \eta_N, \kappa_N$ with at most $N$ rows, and their complementary lower bounds at "good" probability distributions.<br />
<br />
This is a joint work with Belinschi and Guionnet.<br />
<br />
== March 12, 2020, No seminar ==<br />
''' '''<br />
<br />
== March 19, 2020, Spring break ==<br />
''' '''<br />
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== March 26, 2020, CANCELLED, [https://math.cornell.edu/philippe-sosoe Philippe Sosoe] (Cornell) ==<br />
''' '''<br />
<br />
== April 2, 2020, CANCELLED, [http://pages.cs.wisc.edu/~tl/ Tianyu Liu] (UW Madison)==<br />
''' '''<br />
<br />
== April 9, 2020, CANCELLED, [http://stanford.edu/~ajdunl2/ Alexander Dunlap] (Stanford) ==<br />
''' '''<br />
<br />
== April 16, 2020, CANCELLED, [https://statistics.wharton.upenn.edu/profile/dingjian/ Jian Ding] (University of Pennsylvania) ==<br />
''' '''<br />
<br />
== April 22-24, 2020, CANCELLED, [http://frg.int-prob.org/ FRG Integrable Probability] meeting ==<br />
<br />
3-day event in Van Vleck 911<br />
<br />
== April 23, 2020, CANCELLED, [http://www.hairer.org/ Martin Hairer] (Imperial College) ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Colloquia Wolfgang Wasow Lecture] at 4pm in Van Vleck 911<br />
<br />
== April 30, 2020, CANCELLED, [http://willperkins.org/ Will Perkins] (University of Illinois at Chicago) ==<br />
''' '''<br />
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[[Past Seminars]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Probability&diff=19440Probability2020-07-03T15:26:35Z<p>Vadicgor: </p>
<hr />
<div>__NOTOC__<br />
<br />
= '''Probability at UW-Madison''' =<br />
<br />
<br><br />
<br />
== Tenured and tenure-track faculty ==<br />
<br />
[http://www.math.wisc.edu/~anderson/ David Anderson] (Duke, 2005) applied probability, numerical methods, mathematical biology.<br />
<br />
[http://www.math.wisc.edu/~vadicgor/ Vadim Gorin] (Moscow, 2011) integrable probability, random matrices, asymptotic representation theory<br />
<br />
[http://www.math.wisc.edu/~roch/ Sebastien Roch] (UC Berkeley, 2007) applied probability, mathematical biology, theoretical computer science.<br />
<br />
[http://www.math.wisc.edu/~seppalai/ Timo Seppäläinen] (Minnesota, 1991) motion in a random medium, random growth models, interacting particle systems, large deviation theory.<br />
<br />
[http://www.math.wisc.edu/~hshen3/ Hao Shen] (Princeton, 2013) stochastic partial differential equations, mathematical physics, integrable probability<br />
<br />
[http://www.math.wisc.edu/~valko/ Benedek Valko] (Budapest, 2004) interacting particle systems, random matrices.<br />
<br />
<br />
<br />
== Emeriti ==<br />
<br />
[http://psoup.math.wisc.edu/kitchen.html David Griffeath] (Cornell, 1976)<br />
<br />
[http://www.math.wisc.edu/~kuelbs Jim Kuelbs] (Minnesota, 1965)<br />
<br />
[http://www.math.wisc.edu/~kurtz Tom Kurtz] (Stanford, 1967)<br />
<br />
Peter Ney (Columbia, 1961)<br />
<br />
Josh Chover (Michigan, 1952)<br />
<br />
<br />
== Postdocs ==<br />
<br />
Scott Smith (Maryland, 2016)<br />
<br />
<br />
<br />
== Graduate students ==<br />
<br />
<br />
[http://www.math.wisc.edu/~kehlert/ Kurt Ehlert] <br />
<br />
[http://www.math.wisc.edu/~kang Dae Han Kang]<br />
<br />
[https://sites.google.com/a/wisc.edu/brandon-legried/ Brandon Legried]<br />
<br />
Yun Li<br />
<br />
[http://sites.google.com/a/wisc.edu/tung-nguyen/ Tung Nguyen]<br />
<br />
[http://www.math.wisc.edu/~cyuan25/ Chaojie Yuan]<br />
<br />
<br />
<br />
== [[Probability Seminar]] ==<br />
<br />
Thursdays at 2:30pm, VV901<br />
<br />
==[[Graduate student reading seminar]]==<br />
<br />
Email list: join-grad_prob_seminar@lists.wisc.edu<br />
<br />
Tuesdays, 2:30pm, 901 Van Vleck<br />
<br />
== [[Probability group timetable]]==<br />
<br />
== [[Undergraduate courses in probability]]==<br />
<br />
== Graduate Courses in Probability ==<br />
<br />
<br />
<br />
'''2019 Fall'''<br />
<br />
Math/Stat 733 Theory of Probability I<br />
<br />
<br />
<br />
<br />
'''2020 Spring'''<br />
<br />
Math/Stat 734 Theory of Probability II <br />
<br />
Math 833 Topics in Probability</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Past_Probability_Seminars_Spring_2020&diff=19350Past Probability Seminars Spring 20202020-04-12T18:59:39Z<p>Vadicgor: /* April 30, 2020, Will Perkins (University of Illinois at Chicago) */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Spring 2020 =<br />
<br />
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. <br />
<b>We usually end for questions at 3:20 PM.</b><br />
<br />
If you would like to sign up for the email list to receive seminar announcements then please send an email to <br />
[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]<br />
<br />
<br />
== January 23, 2020, [https://www.math.wisc.edu/~seppalai/ Timo Seppalainen] (UW Madison) ==<br />
'''Non-existence of bi-infinite geodesics in the exponential corner growth model<br />
'''<br />
<br />
Whether bi-infinite geodesics exist has been a significant open problem in first- and last-passage percolation since the mid-80s. A non-existence proof in the case of directed planar last-passage percolation with exponential weights was posted by Basu, Hoffman and Sly in November 2018. Their proof utilizes estimates from integrable probability. This talk describes an independent proof completed 10 months later that relies on couplings, coarse graining, and control of geodesics through planarity and increment-stationary last-passage percolation. Joint work with Marton Balazs and Ofer Busani (Bristol).<br />
<br />
== January 30, 2020, [https://www.math.wisc.edu/people/vv-prof-directory Scott Smith] (UW Madison) ==<br />
'''Quasi-linear parabolic equations with singular forcing'''<br />
<br />
The classical solution theory for stochastic ODE's is centered around Ito's stochastic integral. By intertwining ideas from analysis and probability, this approach extends to many PDE's, a canonical example being multiplicative stochastic heat equations driven by space-time white noise. In both the ODE and PDE settings, the solution theory is beyond the scope of classical deterministic theory because of the ambiguity in multiplying a function with a white noise. The theory of rough paths and regularity structures provides a more quantitative understanding of this difficulty, leading to a more refined solution theory which efficiently divides the analytic and probabilistic aspects of the problem, and remarkably, even has an algebraic component.<br />
<br />
In this talk, we will discuss a new application of these ideas to stochastic heat equations where the strength of the diffusion is not constant but random, as it depends locally on the solution. These are known as quasi-linear equations. Our main result yields the deterministic side of a solution theory for these PDE's, modulo a suitable renormalization. Along the way, we identify a formally infinite series expansion of the solution which guides our analysis, reveals a nice algebraic structure, and encodes the counter-terms in the PDE. This is joint work with Felix Otto, Jonas Sauer, and Hendrik Weber.<br />
<br />
== February 6, 2020, [https://sites.google.com/site/cyleeken/ Cheuk-Yin Lee] (Michigan State) ==<br />
'''Sample path properties of stochastic partial differential equations: modulus of continuity and multiple points'''<br />
<br />
In this talk, we will discuss sample path properties of stochastic partial differential equations (SPDEs). We will present a sharp regularity result for the stochastic wave equation driven by an additive Gaussian noise that is white in time and colored in space. We prove the exact modulus of continuity via the property of local nondeterminism. We will also discuss the existence problem for multiple points (or self-intersections) of the sample paths of SPDEs. Our result shows that multiple points do not exist in the critical dimension for a large class of Gaussian random fields including the solution of a linear system of stochastic heat or wave equations.<br />
<br />
== February 13, 2020, [http://www.jelena-diakonikolas.com/ Jelena Diakonikolas] (UW Madison) ==<br />
'''Langevin Monte Carlo Without Smoothness'''<br />
<br />
Langevin Monte Carlo (LMC) is an iterative algorithm used to generate samples from a distribution that is known only up to a normalizing constant. The nonasymptotic dependence of its mixing time on the dimension and target accuracy is understood mainly in the setting of smooth (gradient-Lipschitz) log-densities, a serious limitation for applications in machine learning. We remove this limitation by providing polynomial-time convergence guarantees for a variant of LMC in the setting of non-smooth log-concave distributions. At a high level, our results follow by leveraging the implicit smoothing of the log-density that comes from a small Gaussian perturbation that we add to the iterates of the algorithm and while controlling the bias and variance that are induced by this perturbation.<br />
Based on joint work with Niladri Chatterji, Michael I. Jordan, and Peter L. Bartlett.<br />
<br />
== February 20, 2020, [https://math.berkeley.edu/~pmwood/ Philip Matchett Wood] (UC Berkeley) ==<br />
'''A replacement principle for perturbations of non-normal matrices'''<br />
<br />
There are certain non-normal matrices whose eigenvalues can change dramatically when a small perturbation is added. However, when that perturbation is an iid random matrix, it appears that the eigenvalues become stable after perturbation and only change slightly when further small perturbations are added. Much of the work is this situation has focused on iid random gaussian perturbations. In this talk, we will discuss work on a universality result that allows for consideration of non-gaussian perturbations, and that shows that all perturbations satisfying certain conditions will produce the same limiting eigenvalue measure. Interestingly, this even allows for deterministic perturbations to be considered. Joint work with Sean O'Rourke.<br />
<br />
== February 27, 2020, No seminar ==<br />
''' '''<br />
<br />
== March 5, 2020, [https://www.ias.edu/scholars/jiaoyang-huang Jiaoyang Huang] (IAS) ==<br />
''' Large Deviation Principles via Spherical Integrals'''<br />
<br />
In this talk, I'll explain a framework to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the asymptotics of spherical integrals obtained by Guionnet and Zeitouni. As examples, we obtain <br />
<br />
1) the large deviation principle for the empirical distribution of the diagonal entries of $UB_NU^*$, for a sequence of $N\times N$ diagonal matrices $B_N$ and unitary/orthogonal Haar distributed matrices $U$;<br />
<br />
2) the large deviation upper bound for the empirical eigenvalue distribution of $A_N+UB_NU^*$, for two sequences of $N\times N$ diagonal matrices $A_N, B_N$, and their complementary lower bounds at "good" probability distributions;<br />
<br />
3) the large deviation principle for the Kostka number $K_{\lambda_N \eta_N}$, for two sequences of partitions $\lambda_N, \eta_N$ with at most $N$ rows;<br />
<br />
4) the large deviation upper bound for the Littlewood-Richardson coefficients $c_{\lambda_N \eta_N}^{\kappa_N}$, for three sequences of partitions $\lambda_N, \eta_N, \kappa_N$ with at most $N$ rows, and their complementary lower bounds at "good" probability distributions.<br />
<br />
This is a joint work with Belinschi and Guionnet.<br />
<br />
== March 12, 2020, No seminar ==<br />
''' '''<br />
<br />
== March 19, 2020, Spring break ==<br />
''' '''<br />
<br />
== March 26, 2020, CANCELLED, [https://math.cornell.edu/philippe-sosoe Philippe Sosoe] (Cornell) ==<br />
''' '''<br />
<br />
== April 2, 2020, CANCELLED, [http://pages.cs.wisc.edu/~tl/ Tianyu Liu] (UW Madison)==<br />
''' '''<br />
<br />
== April 9, 2020, CANCELLED, [http://stanford.edu/~ajdunl2/ Alexander Dunlap] (Stanford) ==<br />
''' '''<br />
<br />
== April 16, 2020, CANCELLED, [https://statistics.wharton.upenn.edu/profile/dingjian/ Jian Ding] (University of Pennsylvania) ==<br />
''' '''<br />
<br />
== April 22-24, 2020, CANCELLED, [http://frg.int-prob.org/ FRG Integrable Probability] meeting ==<br />
<br />
3-day event in Van Vleck 911<br />
<br />
== April 23, 2020, CANCELLED, [http://www.hairer.org/ Martin Hairer] (Imperial College) ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Colloquia Wolfgang Wasow Lecture] at 4pm in Van Vleck 911<br />
<br />
== April 30, 2020, CANCELLED, [http://willperkins.org/ Will Perkins] (University of Illinois at Chicago) ==<br />
''' '''<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
[[Past Seminars]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Past_Probability_Seminars_Spring_2020&diff=19302Past Probability Seminars Spring 20202020-03-24T18:51:37Z<p>Vadicgor: /* April 23, 2020, Martin Hairer (Imperial College) */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Spring 2020 =<br />
<br />
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. <br />
<b>We usually end for questions at 3:20 PM.</b><br />
<br />
If you would like to sign up for the email list to receive seminar announcements then please send an email to <br />
[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]<br />
<br />
<br />
== January 23, 2020, [https://www.math.wisc.edu/~seppalai/ Timo Seppalainen] (UW Madison) ==<br />
'''Non-existence of bi-infinite geodesics in the exponential corner growth model<br />
'''<br />
<br />
Whether bi-infinite geodesics exist has been a significant open problem in first- and last-passage percolation since the mid-80s. A non-existence proof in the case of directed planar last-passage percolation with exponential weights was posted by Basu, Hoffman and Sly in November 2018. Their proof utilizes estimates from integrable probability. This talk describes an independent proof completed 10 months later that relies on couplings, coarse graining, and control of geodesics through planarity and increment-stationary last-passage percolation. Joint work with Marton Balazs and Ofer Busani (Bristol).<br />
<br />
== January 30, 2020, [https://www.math.wisc.edu/people/vv-prof-directory Scott Smith] (UW Madison) ==<br />
'''Quasi-linear parabolic equations with singular forcing'''<br />
<br />
The classical solution theory for stochastic ODE's is centered around Ito's stochastic integral. By intertwining ideas from analysis and probability, this approach extends to many PDE's, a canonical example being multiplicative stochastic heat equations driven by space-time white noise. In both the ODE and PDE settings, the solution theory is beyond the scope of classical deterministic theory because of the ambiguity in multiplying a function with a white noise. The theory of rough paths and regularity structures provides a more quantitative understanding of this difficulty, leading to a more refined solution theory which efficiently divides the analytic and probabilistic aspects of the problem, and remarkably, even has an algebraic component.<br />
<br />
In this talk, we will discuss a new application of these ideas to stochastic heat equations where the strength of the diffusion is not constant but random, as it depends locally on the solution. These are known as quasi-linear equations. Our main result yields the deterministic side of a solution theory for these PDE's, modulo a suitable renormalization. Along the way, we identify a formally infinite series expansion of the solution which guides our analysis, reveals a nice algebraic structure, and encodes the counter-terms in the PDE. This is joint work with Felix Otto, Jonas Sauer, and Hendrik Weber.<br />
<br />
== February 6, 2020, [https://sites.google.com/site/cyleeken/ Cheuk-Yin Lee] (Michigan State) ==<br />
'''Sample path properties of stochastic partial differential equations: modulus of continuity and multiple points'''<br />
<br />
In this talk, we will discuss sample path properties of stochastic partial differential equations (SPDEs). We will present a sharp regularity result for the stochastic wave equation driven by an additive Gaussian noise that is white in time and colored in space. We prove the exact modulus of continuity via the property of local nondeterminism. We will also discuss the existence problem for multiple points (or self-intersections) of the sample paths of SPDEs. Our result shows that multiple points do not exist in the critical dimension for a large class of Gaussian random fields including the solution of a linear system of stochastic heat or wave equations.<br />
<br />
== February 13, 2020, [http://www.jelena-diakonikolas.com/ Jelena Diakonikolas] (UW Madison) ==<br />
'''Langevin Monte Carlo Without Smoothness'''<br />
<br />
Langevin Monte Carlo (LMC) is an iterative algorithm used to generate samples from a distribution that is known only up to a normalizing constant. The nonasymptotic dependence of its mixing time on the dimension and target accuracy is understood mainly in the setting of smooth (gradient-Lipschitz) log-densities, a serious limitation for applications in machine learning. We remove this limitation by providing polynomial-time convergence guarantees for a variant of LMC in the setting of non-smooth log-concave distributions. At a high level, our results follow by leveraging the implicit smoothing of the log-density that comes from a small Gaussian perturbation that we add to the iterates of the algorithm and while controlling the bias and variance that are induced by this perturbation.<br />
Based on joint work with Niladri Chatterji, Michael I. Jordan, and Peter L. Bartlett.<br />
<br />
== February 20, 2020, [https://math.berkeley.edu/~pmwood/ Philip Matchett Wood] (UC Berkeley) ==<br />
'''A replacement principle for perturbations of non-normal matrices'''<br />
<br />
There are certain non-normal matrices whose eigenvalues can change dramatically when a small perturbation is added. However, when that perturbation is an iid random matrix, it appears that the eigenvalues become stable after perturbation and only change slightly when further small perturbations are added. Much of the work is this situation has focused on iid random gaussian perturbations. In this talk, we will discuss work on a universality result that allows for consideration of non-gaussian perturbations, and that shows that all perturbations satisfying certain conditions will produce the same limiting eigenvalue measure. Interestingly, this even allows for deterministic perturbations to be considered. Joint work with Sean O'Rourke.<br />
<br />
== February 27, 2020, No seminar ==<br />
''' '''<br />
<br />
== March 5, 2020, [https://www.ias.edu/scholars/jiaoyang-huang Jiaoyang Huang] (IAS) ==<br />
''' Large Deviation Principles via Spherical Integrals'''<br />
<br />
In this talk, I'll explain a framework to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the asymptotics of spherical integrals obtained by Guionnet and Zeitouni. As examples, we obtain <br />
<br />
1) the large deviation principle for the empirical distribution of the diagonal entries of $UB_NU^*$, for a sequence of $N\times N$ diagonal matrices $B_N$ and unitary/orthogonal Haar distributed matrices $U$;<br />
<br />
2) the large deviation upper bound for the empirical eigenvalue distribution of $A_N+UB_NU^*$, for two sequences of $N\times N$ diagonal matrices $A_N, B_N$, and their complementary lower bounds at "good" probability distributions;<br />
<br />
3) the large deviation principle for the Kostka number $K_{\lambda_N \eta_N}$, for two sequences of partitions $\lambda_N, \eta_N$ with at most $N$ rows;<br />
<br />
4) the large deviation upper bound for the Littlewood-Richardson coefficients $c_{\lambda_N \eta_N}^{\kappa_N}$, for three sequences of partitions $\lambda_N, \eta_N, \kappa_N$ with at most $N$ rows, and their complementary lower bounds at "good" probability distributions.<br />
<br />
This is a joint work with Belinschi and Guionnet.<br />
<br />
== March 12, 2020, No seminar ==<br />
''' '''<br />
<br />
== March 19, 2020, Spring break ==<br />
''' '''<br />
<br />
== March 26, 2020, CANCELLED, [https://math.cornell.edu/philippe-sosoe Philippe Sosoe] (Cornell) ==<br />
''' '''<br />
<br />
== April 2, 2020, CANCELLED, [http://pages.cs.wisc.edu/~tl/ Tianyu Liu] (UW Madison)==<br />
''' '''<br />
<br />
== April 9, 2020, CANCELLED, [http://stanford.edu/~ajdunl2/ Alexander Dunlap] (Stanford) ==<br />
''' '''<br />
<br />
== April 16, 2020, CANCELLED, [https://statistics.wharton.upenn.edu/profile/dingjian/ Jian Ding] (University of Pennsylvania) ==<br />
''' '''<br />
<br />
== April 22-24, 2020, CANCELLED, [http://frg.int-prob.org/ FRG Integrable Probability] meeting ==<br />
<br />
3-day event in Van Vleck 911<br />
<br />
== April 23, 2020, CANCELLED, [http://www.hairer.org/ Martin Hairer] (Imperial College) ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Colloquia Wolfgang Wasow Lecture] at 4pm in Van Vleck 911<br />
<br />
== April 30, 2020, [http://willperkins.org/ Will Perkins] (University of Illinois at Chicago) ==<br />
''' '''<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
[[Past Seminars]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Past_Probability_Seminars_Spring_2020&diff=19275Past Probability Seminars Spring 20202020-03-18T05:06:02Z<p>Vadicgor: /* April 2, 2020, Tianyu Liu (UW Madison) */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Spring 2020 =<br />
<br />
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. <br />
<b>We usually end for questions at 3:20 PM.</b><br />
<br />
If you would like to sign up for the email list to receive seminar announcements then please send an email to <br />
[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]<br />
<br />
<br />
== January 23, 2020, [https://www.math.wisc.edu/~seppalai/ Timo Seppalainen] (UW Madison) ==<br />
'''Non-existence of bi-infinite geodesics in the exponential corner growth model<br />
'''<br />
<br />
Whether bi-infinite geodesics exist has been a significant open problem in first- and last-passage percolation since the mid-80s. A non-existence proof in the case of directed planar last-passage percolation with exponential weights was posted by Basu, Hoffman and Sly in November 2018. Their proof utilizes estimates from integrable probability. This talk describes an independent proof completed 10 months later that relies on couplings, coarse graining, and control of geodesics through planarity and increment-stationary last-passage percolation. Joint work with Marton Balazs and Ofer Busani (Bristol).<br />
<br />
== January 30, 2020, [https://www.math.wisc.edu/people/vv-prof-directory Scott Smith] (UW Madison) ==<br />
'''Quasi-linear parabolic equations with singular forcing'''<br />
<br />
The classical solution theory for stochastic ODE's is centered around Ito's stochastic integral. By intertwining ideas from analysis and probability, this approach extends to many PDE's, a canonical example being multiplicative stochastic heat equations driven by space-time white noise. In both the ODE and PDE settings, the solution theory is beyond the scope of classical deterministic theory because of the ambiguity in multiplying a function with a white noise. The theory of rough paths and regularity structures provides a more quantitative understanding of this difficulty, leading to a more refined solution theory which efficiently divides the analytic and probabilistic aspects of the problem, and remarkably, even has an algebraic component.<br />
<br />
In this talk, we will discuss a new application of these ideas to stochastic heat equations where the strength of the diffusion is not constant but random, as it depends locally on the solution. These are known as quasi-linear equations. Our main result yields the deterministic side of a solution theory for these PDE's, modulo a suitable renormalization. Along the way, we identify a formally infinite series expansion of the solution which guides our analysis, reveals a nice algebraic structure, and encodes the counter-terms in the PDE. This is joint work with Felix Otto, Jonas Sauer, and Hendrik Weber.<br />
<br />
== February 6, 2020, [https://sites.google.com/site/cyleeken/ Cheuk-Yin Lee] (Michigan State) ==<br />
'''Sample path properties of stochastic partial differential equations: modulus of continuity and multiple points'''<br />
<br />
In this talk, we will discuss sample path properties of stochastic partial differential equations (SPDEs). We will present a sharp regularity result for the stochastic wave equation driven by an additive Gaussian noise that is white in time and colored in space. We prove the exact modulus of continuity via the property of local nondeterminism. We will also discuss the existence problem for multiple points (or self-intersections) of the sample paths of SPDEs. Our result shows that multiple points do not exist in the critical dimension for a large class of Gaussian random fields including the solution of a linear system of stochastic heat or wave equations.<br />
<br />
== February 13, 2020, [http://www.jelena-diakonikolas.com/ Jelena Diakonikolas] (UW Madison) ==<br />
'''Langevin Monte Carlo Without Smoothness'''<br />
<br />
Langevin Monte Carlo (LMC) is an iterative algorithm used to generate samples from a distribution that is known only up to a normalizing constant. The nonasymptotic dependence of its mixing time on the dimension and target accuracy is understood mainly in the setting of smooth (gradient-Lipschitz) log-densities, a serious limitation for applications in machine learning. We remove this limitation by providing polynomial-time convergence guarantees for a variant of LMC in the setting of non-smooth log-concave distributions. At a high level, our results follow by leveraging the implicit smoothing of the log-density that comes from a small Gaussian perturbation that we add to the iterates of the algorithm and while controlling the bias and variance that are induced by this perturbation.<br />
Based on joint work with Niladri Chatterji, Michael I. Jordan, and Peter L. Bartlett.<br />
<br />
== February 20, 2020, [https://math.berkeley.edu/~pmwood/ Philip Matchett Wood] (UC Berkeley) ==<br />
'''A replacement principle for perturbations of non-normal matrices'''<br />
<br />
There are certain non-normal matrices whose eigenvalues can change dramatically when a small perturbation is added. However, when that perturbation is an iid random matrix, it appears that the eigenvalues become stable after perturbation and only change slightly when further small perturbations are added. Much of the work is this situation has focused on iid random gaussian perturbations. In this talk, we will discuss work on a universality result that allows for consideration of non-gaussian perturbations, and that shows that all perturbations satisfying certain conditions will produce the same limiting eigenvalue measure. Interestingly, this even allows for deterministic perturbations to be considered. Joint work with Sean O'Rourke.<br />
<br />
== February 27, 2020, No seminar ==<br />
''' '''<br />
<br />
== March 5, 2020, [https://www.ias.edu/scholars/jiaoyang-huang Jiaoyang Huang] (IAS) ==<br />
''' Large Deviation Principles via Spherical Integrals'''<br />
<br />
In this talk, I'll explain a framework to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the asymptotics of spherical integrals obtained by Guionnet and Zeitouni. As examples, we obtain <br />
<br />
1) the large deviation principle for the empirical distribution of the diagonal entries of $UB_NU^*$, for a sequence of $N\times N$ diagonal matrices $B_N$ and unitary/orthogonal Haar distributed matrices $U$;<br />
<br />
2) the large deviation upper bound for the empirical eigenvalue distribution of $A_N+UB_NU^*$, for two sequences of $N\times N$ diagonal matrices $A_N, B_N$, and their complementary lower bounds at "good" probability distributions;<br />
<br />
3) the large deviation principle for the Kostka number $K_{\lambda_N \eta_N}$, for two sequences of partitions $\lambda_N, \eta_N$ with at most $N$ rows;<br />
<br />
4) the large deviation upper bound for the Littlewood-Richardson coefficients $c_{\lambda_N \eta_N}^{\kappa_N}$, for three sequences of partitions $\lambda_N, \eta_N, \kappa_N$ with at most $N$ rows, and their complementary lower bounds at "good" probability distributions.<br />
<br />
This is a joint work with Belinschi and Guionnet.<br />
<br />
== March 12, 2020, No seminar ==<br />
''' '''<br />
<br />
== March 19, 2020, Spring break ==<br />
''' '''<br />
<br />
== March 26, 2020, CANCELLED, [https://math.cornell.edu/philippe-sosoe Philippe Sosoe] (Cornell) ==<br />
''' '''<br />
<br />
== April 2, 2020, CANCELLED, [http://pages.cs.wisc.edu/~tl/ Tianyu Liu] (UW Madison)==<br />
''' '''<br />
<br />
== April 9, 2020, CANCELLED, [http://stanford.edu/~ajdunl2/ Alexander Dunlap] (Stanford) ==<br />
''' '''<br />
<br />
== April 16, 2020, CANCELLED, [https://statistics.wharton.upenn.edu/profile/dingjian/ Jian Ding] (University of Pennsylvania) ==<br />
''' '''<br />
<br />
== April 22-24, 2020, CANCELLED, [http://frg.int-prob.org/ FRG Integrable Probability] meeting ==<br />
<br />
3-day event in Van Vleck 911<br />
<br />
== April 23, 2020, [http://www.hairer.org/ Martin Hairer] (Imperial College) ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Colloquia Wolfgang Wasow Lecture] at 4pm in Van Vleck 911<br />
<br />
== April 30, 2020, [http://willperkins.org/ Will Perkins] (University of Illinois at Chicago) ==<br />
''' '''<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
[[Past Seminars]]</div>Vadicgor