# Mathematical Physics Seminar, Mondays

The seminar on mathematical physics will be held on select Mondays and Wednesdays from 12 – 1pm in CMSA Building, 20 Garden Street, Room G10. This year’s Seminar will be organized by Bogdan Stoica and Tsung-ju Lee.

The list of speakers for the upcoming academic year will be posted below and updated as details are confirmed. Titles and abstracts for the talks will be added as they are received.

Date Speaker Title/Abstract

1/27/2020

Lawrence Barrott (Boston College)

Title: Log Gromov–Witten invariants via degenerations

Abstract: A classical question in algebraic geometry asks to count the number of plane curves of degree d meeting a smooth elliptic curve in a single point tangent to order 3d. This question is best reformulated in terms of log Gromov–Witten invariants which I will introduce. By considering the degeneration of the elliptic curve to the toric boundary Navid Nabijou and I provide a localisation formalism to count these curves. We uncover a refined set of enumerative invariants which we believe are related to certain scattering diagram calculations. If time permits I will explain what happens in higher dimension.

2/3/2020

Ignacio Barros (Northeastern University)

Title: On product identities and the Chow rings of holomorphic symplectic varieties

Abstract: For a moduli space $M$ of stable sheaves over a K3 surface $X$, we propose a series of conjectural identities in the Chow rings $CH_\star (M \times X^\ell),\, \ell \geq 1,$ generalizing the classic Beauville–Voisin identity for a K3 surface. We emphasize consequences of the conjecture for the structure of the tautological subring $R_\star (M) \subset CH_\star (M).$ We prove the proposed identities when $M$ is the Hilbert scheme of points on a K3 surface. This is based on joint work with L. Flapan, A. Marian and R. Silversmith.

2/10/2020

Dan Mangoubi
(Einstein Institute of Mathematics)

Title: On eigenvalues and eigenfunctions of the clamped plate

Abstract: A celebrated theorem of C.L. Siegel from 1929 shows that the multiplicity of eigenvalues for the Laplace eigenfunctions on the unit disk is at most two. We study the fourth order clamped plate problem, showing that the multiplicity of eigenvalues is uniformly bounded. Our method is based on new recursion formulas and Siegel–Shidlovskii theory. If time permits, we discuss possible applications also to nodal geometry. The talk is based on a joint work with Yuri Lvovsky.

2/17/2020

President’s Day

2/24/2020

Yingdi Qin (Harvard)

Title: Coisotropic branes on symplectic tori and homological mirror symmetry

Abstract: Homological mirror symmetry (HMS) asserts that the Fukaya category of a symplectic manifold is derived equivalent to the category of coherent sheaves on the mirror complex manifold. Without suitable enlargement (split closure) of the Fukaya category, certain objects of it are missing to prevent HMS from being true. Kapustin and Orlov conjecture that coisotropic branes should be included into the Fukaya category from a physics view point. In this talk, I will construct for linear symplectic tori a version of the Fukaya category including coisotropic branes and show that the usual Fukaya category embeds fully faithfully into it. I will also explain the motivation of the construction through the perspective of Homological mirror symmetry.

3/2/2020

3/9/2020

3/16/2020

3/23/2020

3/30/2020

4/6/2020

4/13/2020

G02

4/20/2020

4/27/2020

G02

5/27/2020

G02

5/4/2020

G02

5/11/2020

G02