Mathematical Physics Seminar, Mondays

Beginning immediately, until at least December 31, all seminars will take place virtually, through Zoom.

The seminar on mathematical physics will be held on Mondays from 10:30 – 11:30am ET. Please email the seminar organizers to learn how toattend. This year’s Seminar will be organized by Yoosik Kim (yoosik@cmsa.fas.harvard.edu), Tsung-Ju Lee (tjlee@cmsa.fas.harvard.edu), and Yang Zhou (yangzhou@cmsa.fas.harvard.edu).

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. 

DateSpeakerTitle/Abstract
9/14/2020Lino Amorim (Kansas State University)Title: Non-commutative Gromov-Witten invariants

Abstract:  I will describe an analogue of Saito’s theory of primitive forms for Calabi-Yau A-infinity categories. Under some conditions on the Hochschild cohomology of the category, this construction recovers the (genus zero) Gromov-Witten invariants of a symplectic manifold from its Fukaya category. This includes many compact toric manifolds, in particular projective spaces.
9/21/2020Yuhan Sun (Rutgers)Title: Displacement energy of Lagrangian 3-spheres

Abstract:  We study local and global Hamiltonian dynamical behaviors of some Lagrangian submanifolds near a Lagrangian sphere S in a symplectic manifold X. When dim S = 2, we show that there is a one-parameter family of Lagrangian tori near S, which are nondisplaceable in X. When dim S = 3, we obtain a new estimate of the displacement energy of S, by estimating the displacement energy of a one-parameter family of Lagrangian tori near S.
9/28/2020Shota Komatsu (CERN)Title: Wilson loops as matrix product states

Abstract:  In this talk, I will discuss a reformulation of the Wilson loop in large N gauge theories in terms of matrix product states. The construction is motivated by the analysis of supersymmetric Wilson loops in the maximally super Yang–Mills theory in four dimensions, but can be applied to any other large N gauge theories and matrix models, although less effective. For the maximally super Yang–Mills theory, one can further perform the computation exactly as a function of ‘t Hooft coupling by combining our formulation with the relation to integrable spin chains. 
10/5/2020Ming Zhang (UBC)Title: Verlinde/Grassmannian correspondence and applications.

Abstract: In the 90s’, Witten gave a physical derivation of an isomorphism between the Verlinde algebra of $GL(n)$ of level $l$ and the quantum cohomology ring of the Grassmannian $\text{Gr}(n,n+l)$. In the joint work arXiv:1811.01377 with Yongbin Ruan, we proposed a K-theoretic generalization of Witten’s work by relating the $\text{GL}_{n}$ Verlinde numbers to the level $l$ quantum K-invariants of the Grassmannian $\text{Gr}(n,n+l)$, and refer to it as the Verlinde/Grassmannian correspondence.

The correspondence was formulated precisely in the aforementioned paper, and we proved the rank 2 case (n=2) there. In this talk, I will discuss the proof for arbitrary rank. A new technical ingredient is the virtual nonabelian localization formula developed by Daniel Halpern-Leistner.  At the end of the talk, I will describe some applications of this correspondence. 
10/12/2020Cancelled -Columbus Day
10/19/2020Ben Gammage (Harvard)Title: 3d mirror symmetry for abelian gauge groups

Abstract: 3d mirror symmetry is a proposed duality relating a pair of 3-dimensional supersymmetric gauge theories. Various consequences of this duality have been heavily explored by representation theorists in recent years, under the name of “symplectic duality”. In joint work in progress with Justin Hilburn, for the case of abelian gauge groups, we provide a fully mathematical explanation of this duality in the form of an equivalence of 2-categories of boundary conditions for topological twists of these theories. We will also discuss some applications to homological mirror symmetry and geometric Langlands duality. 
10/26/2020Cancelled
11/2/2020Haoyu Sun (Berkeley)Title: Double-Janus linear sigma models and generalized quadratic reciprocity 

Abstract: We study the supersymmetric partition function of a 2d linear sigma-model whose target space is a torus with a complex structure that varies along one worldsheet direction and a Kähler modulus that varies along the other. This setup is inspired by the dimensional reduction of a Janus configuration of 4d N=4 U(1) Super-Yang-Mills theory compactified on a mapping torus (T^2 fibered over S^1) times a circle with an SL(2,Z) duality wall inserted on S^1, but our setup has minimal supersymmetry. The partition function depends on two independent elements of SL(2,Z), one describing the duality twist, and the other describing the geometry of the mapping torus. It is topological and can be written as a multivariate quadratic Gauss sum. By calculating the partition function in two different ways, we obtain identities relating different quadratic Gauss sums, generalizing the Landsberg-Schaar relation. These identities are a subset of a collection of identities discovered by F. Deloup. Each identity contains a phase which is an eighth root of unity, and we show how it arises as a Berry phase in the supersymmetric Janus-like configuration. Supersymmetry requires the complex structure to vary along a semicircle in the upper half-plane, as shown by Gaiotto and Witten in a related context, and that semicircle plays an important role in reproducing the correct Berry phase.
11/9/2020An Huang (Brandeis)Titlep-adic strings, Einstein equations, Green’s functions, and Tate’s thesis

Abstract: I shall discuss a recent work on how p-adic strings can produce perturbative quantum gravity, and an adelic physics interpretation of Tate’s thesis. 
11/16/2020
10:00am ET
Matt Kerr (WUSTL)TitleDifferential equations and mixed Hodge structures

Abstract: We report on a new development in asymptotic Hodge theory, arising from work of Golyshev–Zagier and Bloch–Vlasenko, and connected to the Gamma Conjectures in Fano/LG-model mirror symmetry.  The talk will focus exclusively on the Hodge/period-theoretic aspects through two main examples. 
Given a variation of Hodge structure M on a Zariski open in P^1, the periods of the limiting mixed Hodge structures at the punctures are interesting invariants of M.  More generally, one can try to compute these asymptotic invariants for iterated extensions of M by “Tate objects”, which may arise for example from normal functions associated to algebraic cycles. The main point of the talk will be that (with suitable assumptions on M) these invariants are encoded in an entire function called the motivic Gamma function, which is determined by the Picard-Fuchs operator L underlying M. In particular, when L is hypergeometric, this is easy to compute and we get a closed-form answer (and a limiting motive).  In the non-hypergeometric setting, it yields predictions for special values of normal functions; this part of the story is joint with V. Golyshev and T. Sasaki.
11/23/2020

11:30am ET
Kyoung-Seog Lee (U of Miami)Title: Derived categories and motives of moduli spaces of vector bundles on curves

Abstract: Derived categories and motives are important invariants of algebraic varieties invented by Grothendieck and his collaborators around 1960s. In 2005, Orlov conjectured that they will be closely related and now there are several evidences supporting his conjecture. On the other hand, moduli spaces of vector bundles on curves provide attractive and important examples of algebraic varieties and there have been intensive works studying them. In this talk, I will discuss derived categories and motives of moduli spaces of vector bundles on curves. This talk is based on joint works with I. Biswas and T. Gomez.
11/30/2020Zijun Zhou (IPMU)Title: 3d N=2 toric mirror symmetry and quantum K-theory

Abstract: In this talk, I will introduce a new construction for the K-theoretic mirror symmetry of toric varieties/stacks, based on the 3d N=2 mirror symmetry introduced by Dorey-Tong. Given the toric datum, i.e. a  short exact sequence 0 -> Z^k -> Z^n -> Z^{n-k} -> 0, we consider the toric Artin stack of the form [C^n / (C^*)^k]. Its mirror is constructed by taking the Gale dual of the defining short exact sequence. As an analogue of the 3d N=4 case, we consider the K-theoretic I-function, with a suitable level structure, defined by counting parameterized quasimaps from P^1. Under mirror symmetry, the I-functions of a mirror pair are related to each other under the mirror map, which exchanges the K\”ahler and equivariant parameters, and maps q to q^{-1}. This is joint work with Yongbin Ruan and Yaoxiong Wen.
12/7/2020Thomas Grimm(Utrecht)

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

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