• Speaker: François Greer, Stony Brook University
• Title: Enumerative geometry and modular forms
• Date: 01/08/2020
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

Gromov-Witten invariants are counts of holomorphic curves on a smooth projective variety X. When assembled into a generating series, these invariants often produce special functions. A folklore conjecture predicts that when X admits an elliptic fibration, the Gromov-Witten generating functions are quasi-modular forms. I will discuss recent progress on this conjecture and a program to prove it in general.

• Speaker: Tetiana Shcherbyna, Princeton University
• Title: Random matrix theory and supersymmetry techniques
• Date: 01/10/2020
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a spacial structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY) . SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width.

• Speaker: Eli Matzri, Bar-Ilan University
• Title: The vanishing conjecture for Massey products in Galois cohomology
• Date: 01/15/2020
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall

In this talk I will explain what Massey products are and focus on the vanishing conjecture due to Minac and Tan. I will survey the known results and the different methods used to obtain them, focusing on triple Massey products.

• Speaker: Joseph Waldron, Princeton University
• Title: Birational geometry in positive characteristic
• Date: 01/17/2020
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

Birational geometry aims to classify algebraic varieties by breaking them down into elementary building blocks, which may then be studied in more detail. This is conjecturally accomplished via a process called the log minimal model program. The program is now very well developed for varieties over fields of characteristic zero, but many of the most important proof techniques break down outside that situation. In this talk, I will give an overview of the main aims of the log minimal model program, and then focus on recent progress in the classification of varieties defined over fields of positive characteristic.

• Speaker: Pei-Ken Hung, Massachusetts Institute of Technology
• Title: Einstein's gravity and stability of black holes
• Date: 01/24/2020
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

Though Einstein's fundamental theory of general relativity has already celebrated its one hundredth birthday, there are still many outstanding unsolved problems. The Kerr stability conjecture is one of the most important open problems, which posits that the Kerr metrics are stable solutions of the vacuum Einstein equation. Over the past decade, there have been huge advances towards this conjecture based on the study of wave equations in black hole spacetimes and structures in the Einstein equation. In this talk, I will discuss the recent progress in the stability problems with special focus on the wave gauge.

• Speaker: Tony Feng, MIT
• Title: TBA
• Date: 01/29/2020
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Kevin Sackel, Stony Brook
• Title: TBA
• Date: 02/06/2020
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

TBA

• Speaker: Jin Wang, Stony Brook University
• Title: TBD
• Date: 02/07/2020
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall

No abstract available.

• Speaker: Ákos Nagy, Duke University
• Title: TBD
• Date: 02/13/2020
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Spiro Karigiannis, University of Waterloo
• Title: TBD
• Date: 02/20/2020
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Katya Krupchyk, University of California, Irvine
• Title: Inverse boundary problems for semilinear elliptic PDE
• Date: 02/26/2020
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

In this talk we shall discuss recent progress for partial data inverse boundary problems for semilinear elliptic PDE. It turns out that the presence of a nonlinearity allows one to solve inverse problems in situations where the corresponding linear counterpart is open. In the first part of the talk, we shall also discuss some previous work on partial data inverse boundary problems for linear elliptic PDE, focusing on the case of coefficients of low regularity. This talk is based on joint work with Gunther Uhlmann.

• Speaker: Lawrence Craig Evans, UC Berkeley
• Title: TBD
• Date: 02/27/2020
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Laure Saint-Raymond, École normale supérieure de Lyon
• Title: Irreversibility for a hard sphere gas (Second Phillips Lecture)
• Date: 03/10/2020
• Time: 4:00 PM - 5:00 PM
• Place: C304 Wells Hall

Consider a system of small hard spheres, which are initially (almost) independent and identically distributed. Then, in the low density limit, their empirical measure $\frac{1}{N} \sum_{i=1}^N \delta_{x_i(t), v_i(t)}$ converges almost surely to a non reversible dynamics, described by the Boltzmann equation.

• Speaker: Kevin Hughes, University of Bristol
• Title: $L^p$-improving for spherical maximal functions
• Date: 03/11/2020
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall

I will discuss recent work on $L^p$-improving estimates for spherical maximal functions - continuous and discrete. In the continous setting, this is joint work with Anderson, Roos and Seeger building on important work of Seeger-Wainger-Wright. In the discrete setting, these were independently discovered by myself and by Kesler-Lace.

• Speaker: Xuemiao Chen, University of Maryland
• Title: TBD
• Date: 03/19/2020
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: James Murphy, Tufts University
• Title: TBD
• Date: 03/20/2020
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

TBD

• Speaker: Yilin Wang, MIT
• Title: TBA
• Date: 04/01/2020
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Roger Casals, UC Davis
• Title: TBA
• Date: 04/09/2020
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

TBA

• Speaker: Bahar Acu, Northwestern University
• Title: TBD
• Date: 04/23/2020
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

TBD

• Speaker: J. Maurice Rojas, Texas A&M University and NSF
• Title: TBA
• Date: 04/27/2020
• Time: 3:00 PM - 4:00 PM
• Place: C517 Wells Hall

No abstract available.