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 Artan Sheshmani and Yang Zhou.

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
9/10/2018 Xiaomeng Xu, MIT Title: Stokes phenomenon, Yang-Baxter equations and Gromov-Witten theory.

Abstract: This talk will include a general introduction to a linear differential system with singularities, and its relation with symplectic geometry, Yang-Baxter equations, quantum groups and 2d topological field theories.

9/17/2018 Gaetan Borot, Max Planck Institute

Video

Title: A generalization of Mirzakhani’s identity, and geometric recursion

Abstract: McShane obtained in 1991 an identity expressing the function 1 on the Teichmueller space of the once-punctured torus as a sum over simple closed curves. It was generalized to bordered surfaces of all topologies by Mirzakhani in 2005, from which she deduced a topological recursion for the Weil-Petersson volumes. I will present new identities which represent linear statistics of the simple length spectrum as a sum over homotopy class of pairs of pants in a hyperbolic surface, from which one can deduce a topological recursion for their average over the moduli space. This is an example of application of a geometric recursion developed with Andersen and Orantin.

9/24/2018 Yi Xie, Simons Center

Abstract:  In this talk we will show that Khovanov’s sl(3) link homology together with its module structure can be generalized for spatial webs (bipartite trivalent graphs).We will also introduce a variant called pointed sl(3) Khovanov homology. Those two combinatorial invariants  are related to Kronheimer-Mrowka’s instanton invariants $J^\sharp$ and $I^\sharp$ for spatial webs by two spectral sequences. As an application, we will prove that sl(3) Khovanov module and pointed sl(3) Khovanov homology both detect the planar theta graph.

10/01/2018 Don Bejleri, Harvard TBA
10/08/2018 Pei-Ken Hung, MIT
10/15/2018 Chris Gerig, Harvard Title: A geometric interpretation of the Seiberg-Witten invariants

Abstract: Whenever the Seiberg-Witten (SW) invariants of a 4-manifold X are defined, there exist certain 2-forms on X which are symplectic away from some circles. When there are no circles, i.e. X is symplectic, Taubes’ “SW=Gr” theorem asserts that the SW invariants are equal to well-defined counts of J-holomorphic curves (Taubes’ Gromov invariants). In this talk I will describe an extension of Taubes’ theorem to non-symplectic X: there are well-defined counts of J-holomorphic curves in the complement of these circles, which recover the SW invariants. This “Gromov invariant” interpretation was originally conjectured by Taubes in 1995. This talk will involve contact forms and spin-c structures.

10/29/2018 Francois Greer, Simons Center

TBA

11/05/2018 Siqi He, Simons Center TBA
11/12/2018 Yoosik Kim, Boston University TBA
11/19/2018 Yusuf Barış Kartal, MIT
TBA
12/10/2018 Fenglong You, University of Alberta
Title: Relative and orbifold Gromov-Witten theory
Abstract: Given a smooth projective variety X and a smooth divisor D \subset X, one can study the enumerative geometry of counting curves in X with tangency conditions along D. There are two theories associated to it: relative Gromov-Witten invariants of (X,D) and orbifold Gromov-Witten invariants of the r-th root stack X_{D,r}. For sufficiently large r, Abramovich-Cadman-Wise proved that genus zero relative invariants are equal to the genus zero orbifold invariants of root stacks (with a counterexample in genus 1). We prove that higher genus orbifold Gromov-Witten invariants of X_{D,r} are polynomials in r and the constant terms are exactly higher genus relative Gromov-Witten invariants of (X,D). If time permits, I will also talk about further results in genus zero which allows us to study structures of genus zero relative Gromov-Witten theory. This is based on joint work with Hisan-Hua Tseng, Honglu Fan and Longting Wu.

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

 

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