Mathematical Physics Seminar, Mondays

Beginning immediately, until at least April 30, all seminars will take place virtually, through Zoom. A link to attend can be found in the schedule below.

The seminar on mathematical physics will be held on Mondays from 12 – 1pm virtually. Please email the seminar organizers to obtain a link. 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

Mauricio Romo (Tsinghua University)

Video

Title: Enumerative invariants and exponential networks

Abstract: I will define and review the basics of exponential networks associated to CY 3-folds described by conic bundles. I will focus mostly on the mathematical aspects and general ideas behind this construction as well as its conjectural connection with generalized Donaldson–Thomas invariants. This is based on joint work with S. Banerjee and P. Longhi.

3/9/2020

Laure Flapan (MIT)

Title: Fano Lagrangian submanifolds of hyperkahler manifolds

Abstract: For any polarized hyperkahler manifold of K3 type whose dimension is divisible by 8, we produce a Lagrangian submanifold which is Fano arising as a connected component of the fixed locus of an involution on the hyperkahler manifold. This is an ongoing joint work with E. Macrì, K. O’Grady, and G. Saccà.

3/16/2020

Spring Break

 

3/23/2020

Bogdan Stoica (CMSA)

This meeting will be taking place virtually on Zoom.

Title: Bit Threads: Understanding Gravitation from Quantum Entanglement

Abstract: The AdS/CFT correspondence stipulates that gravitational evolution in a bulk spacetime is dual to a boundary description that has no gravity. In the AdS/CFT picture the bulk spacetime evolves gravitationally against an anti-de Sitter space background, and the boundary dual theory is a conformal gauge theory in a spacetime of one dimension less. Recent insights by Ryu and Takayanagi have conjectured that quantum entangled boundary states quantitatively give rise to geometry in the bulk. They do so by explicitly referring to “minimal surfaces” in the bulk, connecting them to the entropy of a related area in the boundary. I will present a conceptually and technically powerful complementary holographic entanglement picture, reformulating Ryu–Takayanagi to no longer refer to minimal surfaces, and suggesting a new way to think about the holographic principle and the connection between spacetime gravitation and information. I will introduce the idea of bit threads, and show how they can be used for fun and profit.

3/30/2020

11:00am

Timothy Large (MIT)

This meeting will be taking place virtually on Zoom.

Title: Floer K-theory and exotic Liouville manifolds

Abstract: In this talk, I will discuss how to define the (wrapped) Fukaya category of an exact symplectic manifold with coefficients in extraordinary cohomology theories, following the ideas of Cohen–Jones–Segal. I will then explain how to construct an exotic symplectic ball, which has vanishing ordinary symplectic homology, but can be distinguished from the standard ball by using Floer homology with coefficients in complex K-theory.

4/6/2020

John Alexander Cruz Morales (Universidad Nacional de Colombia)

This meeting will be taking place virtually on Zoom.

4/13/2020

 

This meeting will be taking place virtually on Zoom.

4/20/2020

 

This meeting will be taking place virtually on Zoom.

4/27/2020

G02

Yu-Wei Fan (Berkeley)

This meeting will be taking place virtually on Zoom.

5/4/2020

G02

 

 

5/11/2020

G02

 

 

For a listing of previous Mathematical Physics Seminars, please click here.

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