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


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 Title: sl(3) Khovanov module and the detection of planar theta-graph

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 Dori Bejleri, MIT Title: Stable pair compactifications of the moduli space of degree one del Pezzo surfaces via elliptic fibrations

Abstract: A degree one del Pezzo surface is the blowup of P^2 at 8 general points. By the classical Cayley-Bacharach Theorem, there is a unique 9th point whose blowup produces a rational elliptic surface with a section. Via this relationship, we can construct a stable pair compactification of the moduli space of anti-canonically polarized degree one del Pezzo surfaces. The KSBA theory of stable pairs (X,D) is the natural extension to dimension 2 of the Deligne-Mumford-Knudsen theory of stable curves. I will discuss the construction of the space of interest as a limit of a space of weighted stable elliptic surface pairs and explain how it relates to some previous compactifications of the space of degree one del Pezzo surfaces. This is joint work with Kenny Ascher.

10/08/2018 Pei-Ken Hung, MIT Title: The linear stability of the Schwarzschild spacetime in the harmonic gauge: odd part

Abstract: We study the odd solution of the linearlized Einstein equation on the Schwarzschild background and in the harmonic gauge. With the aid of Regge-Wheeler quantities, we are able to estimate the odd part of Lichnerowicz d’Alembertian equation. In particular, we prove the solution decays at rate $\tau^{-1+\delta}$ to a linearlized Kerr solution.

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.

10/22/2018 Sze Ning Mak, Brown TBA
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
11/26/2018 Andreas Malmendier, Utah State Title: (1,2) polarized Kummer surfaces and the CHL string

Abstract: A smooth K3 surface obtained as the blow-up of the quotient of a four-torus by the involution automorphism at all 16 fixed points is called a Kummer surface. Kummer surface need not be algebraic, just as the original torus need not be.  However, algebraic Kummer surfaces obtained from abelian varieties provide a fascinating arena for string compactification as they are not trivial spaces but are sufficiently simple for one to be able to analyze most of their properties in detail.

In this talk, we give an explicit description for the relation between algebraic Kummer surfaces of Jacobians of genus-two curves with principal polarization and those associated to (1, 2)-polarized abelian surfaces from three different angles: the point of view of 1) the binational geometry of quartic surfaces in P^3 using even-eights, 2) elliptic fibrations on K3 surfaces of Picard-rank 17 over P^1 using Nikulin involutions, 3) theta-functions of genus-two using two-isogeny.  Finally, we will explain how these (1,2)-polarized Kummer surfaces naturally appear as F-theory backgrounds for the so-called CHL string. (This is joint work with Adrian Clingher.)

12/03/2018 Arnav Tripathy, Harvard 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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