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The Universality Phenomenon for Log-Gas Ensembles

Special Seminar

Come join us on Monday, January 30, 2023 at 04:30pm in room 520, Professor Alisa Knizel (The University of Chicago) will be giving a special lecture titled “The Universality Phenomenon for Log-Gas Ensembles”.

Abstract: Though exactly solvable systems are very special, their asymptotic properties
are believed to be representative for larger families of models. In this way,
besides being interesting in their own right, exactly solvable systems are
exemplars of their conjectured universality classes and can be used to build
intuition and tools, as well as to make predictions. I will illustrate the phenomenon of
universality with the examples from my work on log-gas ensembles.

Location: Mathematics Hall, room 520

Date: Monday, January 30, 2023 at 04:30pm

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Spring 2023 Graduate Topics Courses

The Graduate topics courses for the Spring term are now available.

For more information, please visit the following link: Graduate Topics Courses

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The Many Kinds of Uniformity in Graph Configuration Spaces

Special Seminar

Come join us on Wednesday, January 25, 2023 at 04:30pm in room 520, Professor Eric Ramos (Bowdoin College) will be giving a special lecture titled “The many kinds of uniformity in graph configuration spaces”.

Abstract: For a given topological space X, the (unordered) configuration space of n points on X, F_n(X), is the space of n-element subsets of X. Much of the work on these spaces has considered cases where the underlying space X is a manifold of dimension higher than two. For instance, one famous result of McDuff states that if X is the interior of a compact manifold of dimension at least two with boundary, then for any i the isomorphism class of the homology group H_i(C_n(X)) is independent of n whenever n is big enough. Put more succinctly, if X is a “sufficiently nice” manifold of dimension at least 2, then the configuration spaces C_n(X) exhibit homological stability.

In this talk, we will consider configuration spaces in the cases where X is a graph. That is, when X is 1-dimensional. In this setting we will find that the homology groups H_i(C_n(X)) exhibit extremely regular behaviors in two orthogonal ways. The first, similar to the classical setting, is when X is fixed and n is allowed to grow. In this case we will see that rather than stabilizing, the Betti numbers grow as polynomials in n. The second kind of regular behavior is observed when one fixes n and allows X to vary. In this case we will use extremely powerful structural theorems in graph theory to discover features of the homology groups H_i(C_n(X)) that must be common across all graphs X.

Location: Mathematics Hall, room 520

Date: Wednesday, January 25, 2023 at 04:30pm

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Surfaces and 4-manifolds

Special Seminar

Come join us on Friday, January 20, 2023 at 10:30am in room 520, Professor Kyle Hayden (Rutgers University-Newark) will be giving a special lecture titled “Surfaces and 4-manifolds” (More…).

Abstract: The topology of smooth manifolds is governed largely by geometry in low dimensions and by algebraic topology in high dimensions. The phase transition occurs in dimension four, where continuous and differential topology split apart and “exotic” phenomena emerges. I will begin by describing how this phase transition can be studied via embedded surfaces in4-manifolds, then I will survey recent developments in this area. In particular, I will explain how quantum invariants (such as Khovanov homology)have recently been used to address existence and uniqueness questions about surfaces in 4-manifolds — and what this might imply for foundational questions about 4-manifolds themselves.

Location: Mathematics Hall, room 520

Date: Friday, January 20, 2023 at 10:30am

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“In Memoriam – Igor Krichever”

It is with profound sadness that we write to share the news that Igor Krichever passed away on Thursday December 1, 2022. A funeral service was held on Friday, December 2, at the Plaza Jewish Community Chapel.

Our condolences goes out to all. Professor Krichever was beloved by many and we will always remember him for his great work and kindness.

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January 23: Søren Galatius

Speaker: Søren Galatius

Title: On topological Pontryagin classes

Abstract: The Pontryagin classes of a real vector bundle can be defined via Chern classes of its complexification, and appear in Hirzebruch’s formula for the signature of a smooth 4n-dimensional manifold for example.  It was realized long ago that Pontryagin classes can be defined more generally for topological bundles, that is, bundles with fibers homeomorphic to euclidean spaces, even in the absence of linear structures.  I will recall a bit of the classical theory of Pontryagin classes for topological bundles, and discuss some new developments including joint work with Randal-Williams on algebraic independence.

Where: Mathematics Hall, room 520
When: Monday, January 23, 2023 at 04:30pm

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Professor Daskalopoulos (Columbia University) and Šešum (Rutgers) to Receive 2023 Satter Prize

Mathematics Professors Panagiota Daskalopoulos (Columbia University) and Nataša Šešum (Rutgers University) have been selected to receive the 2023 Ruth Lyttle Satter Prize in Mathematics.

The prize, awarded by the American Mathematical Society every two years, recognizes an outstanding contribution to mathematics research by a woman in the previous six years.

The Satter Prize will be awarded in January 2023 at the Joint Mathematical Meetings, which will be held in Boston.

AMS news website

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November 30: FRANCESCO MAGGI

Speaker: Francesco Maggi

Title: A stability theory for isoperimetric and minimal area problems

Abstract: We offer a non-technical, panoramic view on some old and new results concerning the quantitative description of minimizers and critical points in basic geometric variational problems involving area. In the first part of the talk we review basic results on almost-isoperimetric and almost-constant mean curvature boundaries, both in the Euclidean and in the Riemannian setting. In the second part of the talk, we introduce the approximation of possibly singular minimal surfaces by “soap films” with positve, small volume. Finally, we revisit some of these results in the more physical context of Allen-Cahn surface tension energies, and introduce a new convergence theorem for the diffused interface volume preserving mean curvature flow.

Where: Mathematics Hall, room 520
When: Wednesday, November 30, 2022 at 04:30pm

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November 02: JAMES MAYNARD

Title: Primes, the zeta function and zero density estimates.
Abstract:  If we could prove the Riemann Hypothesis, then there would be several fantastic consequences for our understanding of prime numbers. It turns out that even if the Riemann Hypothesis is false and there are some counterexamples to it, we can still obtain many of these consequences for primes provided the counterexamples are suitably ‘rare’. I’ll talk about this picture and recent joint work on possible patterns of counterexamples. As a consequence of our new approach if the zeros of the zeta function lay on finitely many vertical lines then we obtain several results on primes which are essentially as strong as what the Riemann Hypothesis would imply.

Where: Mathematics Hall, room 520
When: Wednesday, November 02, 2022 at 04:30pm

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Amol Aggarwal Awarded the 2022 Packard Fellowships in Science and Engineering

The Packard Foundation established the Fellowships program in 1988 to provide early-career scientists with flexible funding and the freedom to take risks and explore new frontiers in their fields. Each year, the Foundation invites 54 universities to nominate two faculty members for consideration. The Packard Fellowships Advisory Panel, a group of 12 internationally-recognized scientists and engineers, evaluates the nominations and recommends 20 Fellows for approval by the Packard Foundation Board of Trustees.

Amol Aggarwal is an Associate Professor in the Department of Mathematics at Columbia University. By developing (and often combining) algebraic, analytic, and probabilistic frameworks, Aggarwal studies how intricate structures behave in large scaling limits under various guises, such as statistical mechanical systems with many molecules; random matrices of high dimension; and surfaces of large genus.

For more information please visit: Meet the 2022 Class of Packard Fellows for Science and Engineering – The David and Lucile Packard Foundation

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