Mathematical Physics Seminar, Mondays

The seminar on mathematical physics will be held on select Mondays and Wednesdays from 12 – 1:30pm in CMSA Building, 20 Garden Street, Room G10.

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.

For a listing of Mathematical Physics Seminars held prior to the 2018 Spring Semester, please click here.

Date……… Speaker…………. Title/Abstract
2-5-2018 Hyungchul Kim (Pohang University of Science and Technology) Seiberg duality and superconformal index in 3d

Abstract: I will discuss 3d N=2 supersymmetric gauge theories with a unitary gauge group and two matter fields in the adjoint representation. The low energy spectrum of BPS states of the theory can be studied from the superconformal index. The information on the low energy spectrum including monopole operators is essential to construct a Seiberg-type dual theory. Superconformal indices for a dual pair of the theories should be the same, which is a physical basis for a mathematical identity.

2-12-2018 Matthew Stroffregen

(MIT)

Equivariant Khovanov Spaces

Abstract: Associated to a link L in the three-sphere, Lipshitz-Sarkar constructed a topological space, well-defined up to stable homotopy, whose homology is the (even) Khovanov homology of L.  We extend this to construct an “odd Khovanov space” of L, whose homology recovers odd Khovanov homology. We also equip the odd Khovanov space with a natural involution whose fixed point set is the (even) Khovanov space of Lipshitz-Sarkar, and show that the even Khovanov space admits its own natural involution.  We outline some conjectures relating the even and odd Khovanov spaces. This is joint work with Sucharit Sarkar and Chris Scaduto.

2-26-2018 Jordan Keller

(Harvard)

Linear Stability of Schwarzschild Black Holes

Abstract: The Schwarzschild black holes comprise a static, spherically symmetric family of black hole solutions to the vacuum Einstein equations.  The physical relevance of such solutions is intimately related to their stability under gravitational perturbations. We present results on the linear stability of the Schwarzschild black holes, joint work with Pei-Ken Hung and Mu-Tao Wang.

3-5-2018 Shinobu Hosono (Gakushuin University) Movable vs monodromy nilpotent cones of Calabi-Yau manifolds

abstract: I will show two interesting examples of mirror symmetry of Calabi-Yau complete intersections which have birational automorphisms of infinite order. I will first describe/observe mirror correspondences between the movable cones in birational geometry and the monodromy nilpotent cones which are defined at each boundary points (called LCSLs) in the moduli spaces and naturally glued together. In doing this, I will identify  “Picard-Lefschetzs monodromy transformations for flopping curves” in the mirror families. If time permits, I will show one more example of Calabi-Yau complete intersections for which we observe similar correspondence between the birational geometry and monodromy nilpotent cones. However, in this example, we observe that the correspondence becomes complete when we include a non-toric boundary point in the mirror family.

This is based on a recent paper with H. Takagi (arXiv:170

3-5-2018 Emanuel Scheidegger

(Albert Ludwigs University of Freiburg)

Periods and quasiperiods of modular forms and the mirror quintic at the conifold.

Abstract: We review the theory of periods of modular forms and extend it to quasiperiods. General motivic conjectures predict a relation between periods and quasiperiods of certain weight 4 Hecke eigenforms associated to hypergeometric one-parameter families of Calabi-Yau threefolds. We verify this prediction and discuss some of its implications.

3-19-2018

Room G02

Emanuel Scheidegger

(Albert Ludwigs University of Freiburg)

From Gauged Linear Sigma Models to Landau-Ginzburg orbifolds via central charge functions

Abstract: We review the categorical description of the Calabi-Yau/Landau-Ginzburg correspondence in terms of equivariant matrix factorizations in the gauged linear sigma model. We present the hemisphere partition function as a central charge function in the gauged linear sigma model. We study the relation of this function in the LG phase to the Chern character of equivariant matrix factorizations of the LG potential and generating functions of FJRW invariants.

3-26-2018 Yi Xie

SCGP

Surgery, Polygons and Instanton Floer homology

Abstract: Many classical numerical invariants (including Casson invariant, Alexander polynomial and Jones polynomial) for 3-manifolds or links satisfy surgery formulas relating three different 3-manifolds or links. All those invariants are categorified by certain Floer homologies (or Khovanov homology) which also satisfy so-called surgery exact triangles. In this talk I will discuss the notion of “surgery exact polygons” which appears in the SU(N)-instanton Floer homology theory. Roughly speaking, an “n-gon” is a relation among the Floer homology groups of 3-manifolds obtained by n different Dehn surgeries on a fixed knot. It generalizes the surgery exact triangle in SU(2)-instanton Floer homology. If time permits, I will also talk about a homological-mirror-symmetry-type  conjecture which motivates this work. This is joint work with Lucas Culler and Aliakbar Daemi.

4-2-2018 Cheuk-Yu Mak

Cambridge University

Discrete Legendre transform and tropical multiplicity from symplectic geometry

Abstract:There is a long history of enumerative invariants and related problems in mirror symmetry. One powerful approach to understand it is given by counting tropical curves with multiplicities. Tropical multiplicity formula in dimension two can be easily understood but the generalization to higher dimensions is less transparent. In this talk, we explain the relation between tropical multiplicities and the torsion of the first homology group of the associated Lagrangian submanifolds/cell complexes. It is a preparation talk for the talk “Tropically constructed Lagrangians in mirror quintic threefolds”, which explains the construction of associated Lagrangian submanifolds using degeneration of hypersurface in toric orbifold.It is a joint work with Helge Ruddat.

4-9-2018

Room G02

Brandon B. Meredith

Embry-Riddle Aeronautical University

Mirror Symmetry on Toric Surfaces via Tropical Geometry

Abstract: Mirror symmetry is a curious duality, first noticed by physicists and then excitedly embraced by mathematicians, between certain manifolds and their “mirror” spaces. This talk considers mirror symmetry on toric surfaces, which are varieties with certain convenient combinatorial properties and include many well-known surfaces. These surfaces are especially suited to being exploited by tropical geometry, which is a form of algebraic geometry over the “tropical semi-ring.” This talk will discuss the generalization of mirror symmetry to all toric surfaces (expanded from just the Fano case) following the Gross-Siebert Program wherein singularities are added to the tropical picture in order to pull more curves into view.

4-16-2018 Yuan Gao

Stony Brook

Title: On the extension of the Viterbo functor

Abstract: In this talk I will describe deformations of wrapped Fukaya categories that arise from cobordisms, using which the Viterbo restriction functor can be extended to any exact cylindrical Lagrangian submanifold. I will also discuss how this extension can be viewed from the perspective of Lagrangian correspondences.

4-23-2018

Room G02

Baohua Fu

Chinese Academy of Science

Title: Equivariant compactifications of vector groups

Abstract: In 1954, Hirzebruch raised the problem to classify smooth compactifications of vector spaces with second Betti number 1, which is known till now up to dim 3. In 1999, Hassett-Tschinkel considered the equivariant version of this problem and obtained the classification up to dim. 3. I’ll report recent progress on this (equivariant) problem. In particular, we obtain the classification up to dimension 5.

4-30-2018 Dmitry Tonkonog

UC Berkeley

Title: Geometry of symplectic flux

Abstract: Symplectic flux measures the areas of cylinders swept in the process of an isotopy of a Lagrangian submanifold. This is a classical invariant which captures quantitative aspects of symplectic manifolds. I will report on joint work with Egor Shelukhin and Renato Vianna in which we study the geometry of flux using a technique inspired by mirror symmetry.

 

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