• 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: Brandon Bavier
• Title: An Introduction to Hyperbolic Knot Theory
• Date: 01/22/2020
• Time: 4:00 PM - 5:00 PM
• Place: C517 Wells Hall

When studying knots, it is common to look at their complement to find invariants of the knot. One way to do this is to put a geometric structure on the complement, and look at common geometric invariants, such as volume. In this introductory level talk, we will cover the basics of hyperbolic geometry, and how we can use its properties to find invariants of hyperbolic knots, knots whose complement is hyperbolic.

• Speaker: Felix Janda, IAS, Princeton University
• Title: Enumerative geometry: old and new.
• Date: 01/27/2020
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

For as long as people have studied geometry, they have counted geometric objects. For example, Euclid's Elements starts with the postulate that there is exactly one line passing through two distinct points in the plane. Since then, the kinds of counting problems we are able to pose and to answer has grown. Today enumerative geometry is a rich subject with connections to many fields, including combinatorics, physics, representation theory, number theory and integrable systems. In this talk, I will show how to solve several classical counting questions. I will then move to a more modern problem with roots in string theory which has been the subject of intense study for the last three decades: The computation of the Gromov-Witten invariants of the quintic threefold, an example of a Calabi-Yau manifold

• Speaker: Henri Darmon, McGill
• Title: TBA
• Date: 02/05/2020
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Henri Darmon, McGill University
• Title: TBD
• Date: 02/06/2020
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Yuan Liu, University of Michigan
• Title: TBA
• Date: 02/12/2020
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Chris Henderson, University of Arizona
• Title: TBA
• Date: 02/14/2020
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall

No abstract available.

• Speaker: Jacob Tsimerman, University of Toronto
• Title: TBD
• Date: 02/20/2020
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Aleksander Doan, Columbia University
• Title: TBD
• Date: 02/27/2020
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Laure Saint-Raymond, École normale supérieure de Lyon
• Title: Disorder increases almost surely (First Phillips Lecture)
• Date: 03/09/2020
• Time: 6:30 PM - 7:30 PM
• Place: 105AB Kellogg Center

In the every day life, there are many examples of mixing phenomena : milk and water in a same container will not stay separate from each other, marbles in a bag will not line up spontaneously according to their color, ... In this first talk, we intend to study a simple mathematical model which explains why we can observe spontaneous mixing but not the reverse phenomenon.

• Speaker: Laure Saint-Raymond, École normale supérieure de Lyon
• Title: The structure of correlations (Third Philips Lecture)
• Date: 03/11/2020
• Time: 4:00 PM - 5:00 PM
• Place: C304 Wells Hall

Although the distribution of hard spheres remains essentially chaotic in this low density regime, collisions give birth to small correlations, which keep part of the information. The structure of these dynamical correlations is amazing, going through all scales. This analysis provides actually a characterization of small fluctuations (central limit theorem), and large deviations.

• Speaker: June Huh, Institute for Advanced Study
• Title: TBD
• Date: 03/12/2020
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Dimitri Shlyakhtenko, UCLA
• Title: TBD
• Date: 03/19/2020
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Jianfeng Lu, Duke University
• Title: TBA
• Date: 03/27/2020
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Tan Bui-Thanh, University of Texas at Austin
• Title: TBD
• Date: 04/03/2020
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Adrian Ioana, UC San Diego
• Title: TBD
• Date: 04/09/2020
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Rafe Mazzeo, Stanford University
• Title: TBD
• Date: 04/23/2020
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

No abstract available.