https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Vadicgor&feedformat=atomUW-Math Wiki - User contributions [en]2020-12-05T00:52:55ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=20377Colloquia2020-11-23T03:29:52Z<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 />
'''Symmetries in Algebraic Geometry and Cremona transformations'''<br />
<br />
In this talk I will discuss symmetries of complex algebraic varieties. When studying a projective variety $X$, one usually wants to understand its symmetries. Conversely, the structure of the group of automorphisms of $X$ encodes relevant geometric properties of $X$. After describing some examples of automorphism groups of projective varieties, I will discuss why the notion of automorphism is too rigid in the scope of birational geometry. We are then led to consider another class of symmetries of $X$, its birational self-maps. Birational self-maps of the projective space $\mathbb{P}^n$ are called Cremona transformations. Describing the structure of the group of Cremona transformations of the plane is a classical problem that goes back to the 19th century. In higher dimensions, not so much is known, and a natural problem is to construct interesting subgroups of the Cremona group. I will end by discussing a recent work with Alessio Corti and Alex Massarenti, where we investigate subgroups of the Cremona group consisting of symmetries preserving some special meromorphic volume forms.<br />
<br />
== October 23, 2020, [http://www.math.toronto.edu/quastel/ Jeremy Quastel] (University of Toronto) ==<br />
<br />
(Hosted by Gorin)<br />
<br />
'''Towards KPZ Universality'''<br />
<br />
The 1-d KPZ universality class contains random interface growth models<br />
as well as random polymer free energies and driven diffusive systems. <br />
The KPZ fixed point has now been determined, through the exact solution of a special model<br />
in the class, TASEP, and is expected to describe the asymptotic fluctuations for all models in the class.<br />
It is an integrable Markov process, with transition probabilities described by a system of integrable PDE’s. <br />
Very recently, new techniques have become available to prove <br />
the convergence of the KPZ equation itself, as well as some non-integrable extensions<br />
of TASEP, to the KPZ fixed point. This talk will be a gentle introduction to these developments<br />
with no prior knowledge assumed. The results are, variously, joint works with <br />
Daniel Remenik, Konstantin Matetski, and Sourav Sarkar.<br />
<br />
== November 6, 2020, [http://math.jhu.edu/~sakellar/ Yiannis Sakellaridis] (Johns Hopkins University)==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
'''Harmonic analysis, intersection cohomology, and L-functions.'''<br />
<br />
The goal of this lecture will be to describe a link between geometric-topological objects (certain intersection complexes on singular loop spaces), and objects of arithmetic interest (L-functions). The link between the two is by a Fourier/spectral transform. I will begin by giving an overview of Iwasawa–Tate theory, which expresses the Riemann zeta function as the Mellin transform of a certain theta series, and will conclude by describing joint work with Jonathan Wang (MIT), which expresses other L-functions as spectral transforms of functions obtained from intersection complexes on singular arc spaces. No prior familiarity with notions such as L-functions or intersection cohomology will be assumed.<br />
<br />
== November 20, 2020, [https://web.ma.utexas.edu/users/ntran/ Ngoc Mai Tran] (University of Texas) ==<br />
<br />
(Hosted by Rodriguez)<br />
<br />
'''Does your problem have a tropical solution?'''<br />
<br />
Tropical mathematics is mathematics done in the min-plus (or max-plus) algebra.<br />
The power of tropical mathematics comes from two key ideas: (a) tropical objects are limits of classical ones, and (b) the geometry of tropical objects is polyhedral. In this talk I'll demonstrate how these two ideas are used to solve a variety of problems in different domains the last 10 years, from deep neural networks, semigroups theory, auction theory and extreme value statistics.<br />
<br />
== December 4, 2020, [http://math.sfsu.edu/federico/ Federico Ardila] (San Francisco) ==<br />
<br />
(Hosted by Ellenberg)<br />
<br />
'''Measuring polytopes through their algebraic structure.'''<br />
<br />
Generalized permutahedra are a beautiful family of polytopes with a rich combinatorial structure, and strong connections to optimization and algebraic geometry. We prove they are the universal family of polyhedra with a certain Hopf-algebraic structure. This Hopf-algebraic structure is compatible with McMullen’s foundational work on the polytope algebra.<br />
<br />
Our construction provides a unifying framework to organize and study many combinatorial families; for example:<br />
<br />
1. It uniformly answers open questions and recovers known results about graphs, posets, matroids, hypergraphs, simplicial complexes, and others.<br />
<br />
2. It shows that permutahedra and associahedra “know" how to compute the multiplicative and compositional inverses of power series.<br />
<br />
3. It explains the mysterious fact that many combinatorial invariants of matroids, posets, and graphs can also be thought of as measures on polytopes, satisfying the inclusion-exclusion relations.<br />
<br />
This is joint work with Marcelo Aguiar (2017) and Mario Sanchez (2020).<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=20376Colloquia2020-11-23T03:29:34Z<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 />
'''Symmetries in Algebraic Geometry and Cremona transformations'''<br />
<br />
In this talk I will discuss symmetries of complex algebraic varieties. When studying a projective variety $X$, one usually wants to understand its symmetries. Conversely, the structure of the group of automorphisms of $X$ encodes relevant geometric properties of $X$. After describing some examples of automorphism groups of projective varieties, I will discuss why the notion of automorphism is too rigid in the scope of birational geometry. We are then led to consider another class of symmetries of $X$, its birational self-maps. Birational self-maps of the projective space $\mathbb{P}^n$ are called Cremona transformations. Describing the structure of the group of Cremona transformations of the plane is a classical problem that goes back to the 19th century. In higher dimensions, not so much is known, and a natural problem is to construct interesting subgroups of the Cremona group. I will end by discussing a recent work with Alessio Corti and Alex Massarenti, where we investigate subgroups of the Cremona group consisting of symmetries preserving some special meromorphic volume forms.<br />
<br />
== October 23, 2020, [http://www.math.toronto.edu/quastel/ Jeremy Quastel] (University of Toronto) ==<br />
<br />
(Hosted by Gorin)<br />
<br />
'''Towards KPZ Universality'''<br />
<br />
The 1-d KPZ universality class contains random interface growth models<br />
as well as random polymer free energies and driven diffusive systems. <br />
The KPZ fixed point has now been determined, through the exact solution of a special model<br />
in the class, TASEP, and is expected to describe the asymptotic fluctuations for all models in the class.<br />
It is an integrable Markov process, with transition probabilities described by a system of integrable PDE’s. <br />
Very recently, new techniques have become available to prove <br />
the convergence of the KPZ equation itself, as well as some non-integrable extensions<br />
of TASEP, to the KPZ fixed point. This talk will be a gentle introduction to these developments<br />
with no prior knowledge assumed. The results are, variously, joint works with <br />
Daniel Remenik, Konstantin Matetski, and Sourav Sarkar.<br />
<br />
== November 6, 2020, [http://math.jhu.edu/~sakellar/ Yiannis Sakellaridis] (Johns Hopkins University)==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
'''Harmonic analysis, intersection cohomology, and L-functions.'''<br />
<br />
The goal of this lecture will be to describe a link between geometric-topological objects (certain intersection complexes on singular loop spaces), and objects of arithmetic interest (L-functions). The link between the two is by a Fourier/spectral transform. I will begin by giving an overview of Iwasawa–Tate theory, which expresses the Riemann zeta function as the Mellin transform of a certain theta series, and will conclude by describing joint work with Jonathan Wang (MIT), which expresses other L-functions as spectral transforms of functions obtained from intersection complexes on singular arc spaces. No prior familiarity with notions such as L-functions or intersection cohomology will be assumed.<br />
<br />
== November 20, 2020, [https://web.ma.utexas.edu/users/ntran/ Ngoc Mai Tran] (University of Texas) ==<br />
<br />
(Hosted by Rodriguez)<br />
<br />
'''Does your problem have a tropical solution?'''<br />
<br />
Tropical mathematics is mathematics done in the min-plus (or max-plus) algebra.<br />
The power of tropical mathematics comes from two key ideas: (a) tropical objects are limits of classical ones, and (b) the geometry of tropical objects is polyhedral. In this talk I'll demonstrate how these two ideas are used to solve a variety of problems in different domains the last 10 years, from deep neural networks, semigroups theory, auction theory and extreme value statistics.<br />
<br />
== December 4, 2020, [http://math.sfsu.edu/federico/ Federico Ardila] (San Francisco) ==<br />
<br />
(Hosted by Ellenberg)<br />
<br />
'''Measuring polytopes through their algebraic structure'''<br />
<br />
Generalized permutahedra are a beautiful family of polytopes with a rich combinatorial structure, and strong connections to optimization and algebraic geometry. We prove they are the universal family of polyhedra with a certain Hopf-algebraic structure. This Hopf-algebraic structure is compatible with McMullen’s foundational work on the polytope algebra.<br />
<br />
Our construction provides a unifying framework to organize and study many combinatorial families; for example:<br />
<br />
1. It uniformly answers open questions and recovers known results about graphs, posets, matroids, hypergraphs, simplicial complexes, and others.<br />
<br />
2. It shows that permutahedra and associahedra “know" how to compute the multiplicative and compositional inverses of power series.<br />
<br />
3. It explains the mysterious fact that many combinatorial invariants of matroids, posets, and graphs can also be thought of as measures on polytopes, satisfying the inclusion-exclusion relations.<br />
<br />
This is joint work with Marcelo Aguiar (2017) and Mario Sanchez (2020).<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=20220Colloquia2020-10-27T16:05:45Z<p>Vadicgor: /* November 6, 2020, Yiannis Sakellaridis (Johns Hopkins University) */</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 />
'''Symmetries in Algebraic Geometry and Cremona transformations'''<br />
<br />
In this talk I will discuss symmetries of complex algebraic varieties. When studying a projective variety $X$, one usually wants to understand its symmetries. Conversely, the structure of the group of automorphisms of $X$ encodes relevant geometric properties of $X$. After describing some examples of automorphism groups of projective varieties, I will discuss why the notion of automorphism is too rigid in the scope of birational geometry. We are then led to consider another class of symmetries of $X$, its birational self-maps. Birational self-maps of the projective space $\mathbb{P}^n$ are called Cremona transformations. Describing the structure of the group of Cremona transformations of the plane is a classical problem that goes back to the 19th century. In higher dimensions, not so much is known, and a natural problem is to construct interesting subgroups of the Cremona group. I will end by discussing a recent work with Alessio Corti and Alex Massarenti, where we investigate subgroups of the Cremona group consisting of symmetries preserving some special meromorphic volume forms.<br />
<br />
== October 23, 2020, [http://www.math.toronto.edu/quastel/ Jeremy Quastel] (University of Toronto) ==<br />
<br />
(Hosted by Gorin)<br />
<br />
'''Towards KPZ Universality'''<br />
<br />
The 1-d KPZ universality class contains random interface growth models<br />
as well as random polymer free energies and driven diffusive systems. <br />
The KPZ fixed point has now been determined, through the exact solution of a special model<br />
in the class, TASEP, and is expected to describe the asymptotic fluctuations for all models in the class.<br />
It is an integrable Markov process, with transition probabilities described by a system of integrable PDE’s. <br />
Very recently, new techniques have become available to prove <br />
the convergence of the KPZ equation itself, as well as some non-integrable extensions<br />
of TASEP, to the KPZ fixed point. This talk will be a gentle introduction to these developments<br />
with no prior knowledge assumed. The results are, variously, joint works with <br />
Daniel Remenik, Konstantin Matetski, and Sourav Sarkar.<br />
<br />
== November 6, 2020, [http://math.jhu.edu/~sakellar/ Yiannis Sakellaridis] (Johns Hopkins University)==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
'''Harmonic analysis, intersection cohomology, and L-functions.'''<br />
<br />
The goal of this lecture will be to describe a link between geometric-topological objects (certain intersection complexes on singular loop spaces), and objects of arithmetic interest (L-functions). The link between the two is by a Fourier/spectral transform. I will begin by giving an overview of Iwasawa–Tate theory, which expresses the Riemann zeta function as the Mellin transform of a certain theta series, and will conclude by describing joint work with Jonathan Wang (MIT), which expresses other L-functions as spectral transforms of functions obtained from intersection complexes on singular arc spaces. No prior familiarity with notions such as L-functions or intersection cohomology will be assumed.<br />
<br />
== November 20, 2020, [https://web.ma.utexas.edu/users/ntran/ Ngoc Mai Tran] (University of Texas) ==<br />
<br />
(Hosted by Rodriguez)<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=20111Colloquia2020-10-12T00:35:03Z<p>Vadicgor: /* October 23, 2020, Jeremy Quastel (University of Toronto) */</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 />
'''Symmetries in Algebraic Geometry and Cremona transformations'''<br />
<br />
In this talk I will discuss symmetries of complex algebraic varieties. When studying a projective variety $X$, one usually wants to understand its symmetries. Conversely, the structure of the group of automorphisms of $X$ encodes relevant geometric properties of $X$. After describing some examples of automorphism groups of projective varieties, I will discuss why the notion of automorphism is too rigid in the scope of birational geometry. We are then led to consider another class of symmetries of $X$, its birational self-maps. Birational self-maps of the projective space $\mathbb{P}^n$ are called Cremona transformations. Describing the structure of the group of Cremona transformations of the plane is a classical problem that goes back to the 19th century. In higher dimensions, not so much is known, and a natural problem is to construct interesting subgroups of the Cremona group. I will end by discussing a recent work with Alessio Corti and Alex Massarenti, where we investigate subgroups of the Cremona group consisting of symmetries preserving some special meromorphic volume forms.<br />
<br />
== October 23, 2020, [http://www.math.toronto.edu/quastel/ Jeremy Quastel] (University of Toronto) ==<br />
<br />
(Hosted by Gorin)<br />
<br />
'''Towards KPZ Universality'''<br />
<br />
The 1-d KPZ universality class contains random interface growth models<br />
as well as random polymer free energies and driven diffusive systems. <br />
The KPZ fixed point has now been determined, through the exact solution of a special model<br />
in the class, TASEP, and is expected to describe the asymptotic fluctuations for all models in the class.<br />
It is an integrable Markov process, with transition probabilities described by a system of integrable PDE’s. <br />
Very recently, new techniques have become available to prove <br />
the convergence of the KPZ equation itself, as well as some non-integrable extensions<br />
of TASEP, to the KPZ fixed point. This talk will be a gentle introduction to these developments<br />
with no prior knowledge assumed. The results are, variously, joint works with <br />
Daniel Remenik, Konstantin Matetski, and Sourav Sarkar.<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, [https://web.ma.utexas.edu/users/ntran/ Ngoc Mai Tran] (University of Texas) ==<br />
<br />
(Hosted by Rodriguez)<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=Probability_Seminar&diff=20089Probability Seminar2020-10-06T23:24:31Z<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. [https://uwmadison.zoom.us/j/91828707031?pwd=YUJXMUJkMDlPR0VRdkRCQVJtVndIdz09 ZOOM LINK]<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] (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] (Harvard) ==<br />
<br />
'''Large deviations for dense random graphs: beyond mean-field'''<br />
<br />
In a seminal paper, Chatterjee and Varadhan derived an Erdős-Rényi random graph, viewed as a random graphon. This directly provides LDPs for continuous functionals such as subgraph counts, spectral norms, etc. In contrast, very little is understood about this problem if the underlying random graph is inhomogeneous or constrained.<br />
<br />
In this talk, we will explore large deviations for dense random graphs, beyond the “mean-field” setting. In particular, we will study large deviations for uniform random graphs with given degrees, and a family of dense block model<br />
random graphs. We will establish the LDP in each case, and identify the rate function. In the block model setting, we will use this LDP to study the upper tail problem for homomorphism densities of regular sub-graphs. Our results establish that this problem exhibits a symmetry/symmetry-breaking transition, similar to one observed for Erdős-Rényi random graphs.<br />
<br />
Based on joint works with Christian Borgs, Jennifer Chayes, Souvik Dhara, Julia Gaudio and Samantha Petti.<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 />
==October 29, 2020, [https://www.math.wisc.edu/node/80 Yun Li] (UW Madison) ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
== November 5, 2020, [http://sayan.web.unc.edu/ Sayan Banerjee] (UNC at Chapel Hill) ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
== November 12, 2020, [https://cims.nyu.edu/~ajd594/ Alexander Dunlap] (NYU Courant Institute) ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
== November 19, 2020, [https://statistics.wharton.upenn.edu/profile/dingjian/ Jian Ding] (University of Pennsylvania) ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
== December 3, 2020, Tatyana Shcherbina (UW-Madison) ==<br />
<br />
Title: '''TBA'''<br />
<br />
Abstract: TBA<br />
<br />
== December 10, 2020, [https://www.ewbates.com/ Erik Bates] (UW-Madison) ==<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=20019Colloquia2020-09-29T01:25:12Z<p>Vadicgor: /* October 9, 2020, Carolina Araujo (IMPA) */</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 />
'''Symmetries in Algebraic Geometry and Cremona transformations'''<br />
<br />
In this talk I will discuss symmetries of complex algebraic varieties. When studying a projective variety $X$, one usually wants to understand its symmetries. Conversely, the structure of the group of automorphisms of $X$ encodes relevant geometric properties of $X$. After describing some examples of automorphism groups of projective varieties, I will discuss why the notion of automorphism is too rigid in the scope of birational geometry. We are then led to consider another class of symmetries of $X$, its birational self-maps. Birational self-maps of the projective space $\mathbb{P}^n$ are called Cremona transformations. Describing the structure of the group of Cremona transformations of the plane is a classical problem that goes back to the 19th century. In higher dimensions, not so much is known, and a natural problem is to construct interesting subgroups of the Cremona group. I will end by discussing a recent work with Alessio Corti and Alex Massarenti, where we investigate subgroups of the Cremona group consisting of symmetries preserving some special meromorphic volume forms.<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=20018Colloquia2020-09-29T01:25:04Z<p>Vadicgor: /* October 9, 2020, Carolina Araujo (IMPA) */</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 />
```Symmetries in Algebraic Geometry and Cremona transformations'''<br />
<br />
In this talk I will discuss symmetries of complex algebraic varieties. When studying a projective variety $X$, one usually wants to understand its symmetries. Conversely, the structure of the group of automorphisms of $X$ encodes relevant geometric properties of $X$. After describing some examples of automorphism groups of projective varieties, I will discuss why the notion of automorphism is too rigid in the scope of birational geometry. We are then led to consider another class of symmetries of $X$, its birational self-maps. Birational self-maps of the projective space $\mathbb{P}^n$ are called Cremona transformations. Describing the structure of the group of Cremona transformations of the plane is a classical problem that goes back to the 19th century. In higher dimensions, not so much is known, and a natural problem is to construct interesting subgroups of the Cremona group. I will end by discussing a recent work with Alessio Corti and Alex Massarenti, where we investigate subgroups of the Cremona group consisting of symmetries preserving some special meromorphic volume forms.<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=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 />
<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=19552Colloquia2020-08-15T02:29:08Z<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 />
<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 />
<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=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 />
<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=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 />
<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 />
<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=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 />
<br />
<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 />
<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=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 />
<br />
<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 />
<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=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 />
<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]]<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=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 />
<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]]<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 />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<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=19544Colloquia2020-08-15T02:11:33Z<p>Vadicgor: Vadicgor moved page Colloquia to Colloquia/Spring2020</p>
<hr />
<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>
<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 3, 2020, [https://math.wisc.edu TBA] (TBA) ==<br />
'''TBA<br />
'''<br />
<br />
<br />
== September 10, 2020, ==<br />
<br />
<br />
<br />
<br />
[[Past Seminars]]</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php?title=Past_Seminars&diff=19538Past Seminars2020-08-12T22:20:54Z<p>Vadicgor: </p>
<hr />
<div>[[Probability Seminar | Back to Current Probability Seminar Schedule ]]<br />
<br />
[[Past Probability Seminars Spring 2020]]<br />
<br />
[[Past Probability Seminars Fall 2019]]<br />
<br />
[[Past Probability Seminars Spring 2019]]<br />
<br />
[[Past Probability Seminars Fall 2018]]<br />
<br />
[[Past Probability Seminars Spring 2018]]<br />
<br />
[[Past Probability Seminars Fall 2017]]<br />
<br />
[[Past Probability Seminars Spring 2017]]<br />
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[[Past Probability Seminars Fall 2016]]<br />
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[[Past Probability Seminars Spring 2016]]<br />
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[[Past Probability Seminars Fall 2015]]<br />
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[[Past Probability Seminars Spring 2015]]<br />
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[[Past Probability Seminars Fall 2014]]<br />
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[[Past Probability Seminars Spring 2014]]<br />
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[[Past Probability Seminars Fall 2013]]<br />
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[[Past Probability Seminars Spring 2013]]<br />
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[[Past Probability Seminars Fall 2012]]<br />
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[[Past Probability Seminars Spring 2012]]<br />
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[[Past Probability Seminars Fall 2011]]<br />
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[[Past Probability Seminars Spring 2011]]<br />
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[[Past Probability Seminars Fall 2010]]<br />
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[[Past Probability Seminars Spring 2010]]<br />
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[[Past Probability Seminars Fall 2009]]<br />
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[[Past Probability Seminars Spring 2009]]<br />
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[[Past Probability Seminars Fall 2008]]<br />
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[[Past Probability Seminars Spring 2008]]<br />
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[[Past Probability Seminars Fall 2007]]<br />
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[[Past Probability Seminars Spring 2007]]<br />
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[[Past Probability Seminars Fall 2006]]<br />
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[[Past Probability Seminars Spring 2006]]<br />
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[[Past Probability Seminars Fall 2005]]<br />
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[[Past Probability Seminars Spring 2005]]<br />
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[[Past Probability Seminars Fall 2004]]<br />
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[[Past Probability Seminars Spring 2004]]<br />
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[[Past Probability Seminars Fall 2003]]<br />
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[[Past Probability Seminars Spring 2003]]<br />
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[[Past Probability Seminars Fall 2002]]<br />
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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>
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<div>__NOTOC__<br />
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= Spring 2020 =<br />
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<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 />
[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]<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=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>Vadicgor