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, YangBaxter equations and GromovWitten theory.
Abstract: This talk will include a general introduction to a linear differential system with singularities, and its relation with symplectic geometry, YangBaxter 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 oncepunctured 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 WeilPetersson 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 thetagraph
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 KronheimerMrowka’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 CayleyBacharach 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 anticanonically polarized degree one del Pezzo surfaces. The KSBA theory of stable pairs (X,D) is the natural extension to dimension 2 of the DeligneMumfordKnudsen 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  PeiKen 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 ReggeWheeler 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 SeibergWitten invariants
Abstract: Whenever the SeibergWitten (SW) invariants of a 4manifold X are defined, there exist certain 2forms 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 welldefined counts of Jholomorphic curves (Taubes’ Gromov invariants). In this talk I will describe an extension of Taubes’ theorem to nonsymplectic X: there are welldefined counts of Jholomorphic 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 spinc structures. 
10/22/2018
*Room G02* 
Sze Ning Mak, Brown 
Abstract: In this talk, I will review the supersymmetry algebra. For Lie algebras, the concepts of weights and roots play an important role in the classification of representations. The lack of linear “eigenequations” in supersymmetry leads to the failure to realize the JordanChevalley decomposition of ordinary Lie algebras on the supersymmetry algebra. Therefore, we introduce the concept “holoraumy” for the 4D, $\mathcal{N}$extended supersymmetry algebras, which allows us to explore the possible representations of supersymmetric systems of a specified size. The coefficients of the holoraumy tensors for different representations of the same size form a lattice space. For 4D, $\mathcal{N}=1$ minimal supermultiplets (4 bosons + 4 fermions), a tetrahedron is found in a 3D subspace of the 4D lattice parameter space. For 4D, $\mathcal{N}=2$ minimal supermultiplets (8 bosons + 8 fermions), 4 tetrahedrons are found in 4 different 3D subspaces of a 16D lattice parameter space.

10/29/2018  Francois Greer, Simons Center  Title: Rigid Varieties with Lagrangian Spheres
Abstract: Let X be a smooth complex projective variety with its induced Kahler structure. If X admits an algebraic degeneration to a nodal variety, then X contains a Lagrangian sphere as the vanishing cycle. Donaldson asked whether the converse holds. We answer this question in the negative by constructing rigid complex threefolds with Lagrangian spheres using Teichmuller curves in genus 2. 
11/05/2018  Siqi He, Simons Center 
Abstract: We will discuss a Witten’s gauge theory program to define Jones polynomial and Khovanov homology for knots inside of general 3manifolds by counting singular solutions to the KapustinWitten or HaydysWitten equations. We will prove that the dimension reduction of the solutions moduli space to the KapustinWitten equations can be identified with BeilinsonDrinfeld Opers moduli space. We will also discuss the relationship between the Opers and a symplectic geometry approach to define the Khovanov homology for 3manifolds. This is joint work with Rafe Mazzeo.

11/12/2018  No Seminar  
11/19/2018  Yusuf Barış Kartal, MIT 
Abstract: The purpose of this talk is to produce examples of symplectic fillings that cannot be distinguished by the dynamical invariants at a geometric level, but that can be distinguished by the dynamics and deformation theory of (wrapped) Fukaya categories. More precisely, given a Weinstein domain $M$ and a compactly supported symplectomorphism $\phi$, one can produce another Weinstein domain $T_\phi$\textbf{the open symplectic maping torus}. Its contact boundary is independent of $\phi$ and it is the same as the boundary of $T_0\times M$, where $T_0$ is the once punctured torus. We will outline a method to distinguish $T_\phi$ from $T_0\times M$. This will involve the construction of a mirror symmetry inspired algebrogeometric model related to Tate curve for the Fukaya category of $T_\phi$ and exploitation of dynamics on these models to distinguish them.

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 blowup of the quotient of a fourtorus 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 genustwo 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 eveneights, 2) elliptic fibrations on K3 surfaces of Picardrank 17 over P^1 using Nikulin involutions, 3) thetafunctions of genustwo using twoisogeny. Finally, we will explain how these (1,2)polarized Kummer surfaces naturally appear as Ftheory backgrounds for the socalled CHL string. (This is joint work with Adrian Clingher.) 
12/03/2018  Monica Pate, Harvard  TBA 
12/10/2018  Fenglong You, University of Alberta  Title: Relative and orbifold GromovWitten 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 GromovWitten invariants of (X,D) and orbifold GromovWitten invariants of the rth root stack X_{D,r}. For sufficiently large r, AbramovichCadmanWise 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 GromovWitten invariants of X_{D,r} are polynomials in r and the constant terms are exactly higher genus relative GromovWitten 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 GromovWitten theory. This is based on joint work with HisanHua Tseng, Honglu Fan and Longting Wu. 
For a listing of previous Mathematical Physics Seminars, please click here.