# Mathematical Physics Seminar, Wednesdays

The seminar on mathematical physics will be held on Wednesday 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.

 Date Name Title/Abstract 09-04-17 No Talk 09-11-2017 Yu-Shen Lin (Harvad CMSA) Title: From the Decomposition of Picard-Lefschetz Transformation to Tropical Geometry Abstract: Picard-Lefschetz transformation tells the monodromy of a fibration with “good” singular fibres. In the case of fibres are Lagrangian in a symplectic $4$-manifold, there is a natural decomposition of Picard-Lefschetz transformation into two elementary transformations from Floer theory. The idea will help to develop the tropical geometry for some hyperKahler surfaces. 09-18-17 Yoosik Kim (Boston University) Abstract: As an attempt to classify Lagrangian submanifolds and due to their importance in Floer theory, monotone Lagrangian tori have been got attention. In this talk, we provide a way producing monotone Lagrangian tori in the cotangent bundles of some manifolds including spheres or unitary groups. The construction is based on the classification of Lagrangian fibers of a certain completely integrable system on a partial flag manifolds of various types. We then discuss when their Floer cohomologies (under a certain deformation by non-unitary flat line bundles) do not vanish. This talk is based on joint work with Yunhyung Cho and Yong-Geun Oh. 09-27-17 Yu-Wei Fan (Harvard) Abstract: Inspired by mirror symmetry, we define Weil-Petersson geometry on the space of Bridgeland stability conditions on a Calabi-Yau category. The goal is to further understand the stringy Kahler moduli space of Calabi-Yau manifolds.  This is a joint work with A. Kanazawa and S.-T. Yau. 10-04-17 Dingxin Zhang, Brandeis Title: <1 part of slopes under degeneration” Abstract: For a smooth family of projective varieties over a field of characteristic p > 0, it is known that the Newton polygon of fibers goes up under specialization. In this talk, we will show that when the family acquires singular members, the less than one part of the slopes of the Newton polygon goes up under specialization. This could be viewed as a characteristic p analogue of a simple phenomenon in Hodge theory. 10-11-17 No Talk 10-18-2017 Nati Blaier, Harvard CMSA Title: Geometry of the symplectic Torelli group Abstract: This talk has two parts. In the first part of the talk, I will introduce the group of symplectomorphism and try to convince you that it is a very important object in symplectic topology by surveying some known structural results and drawing a comparison with the situation in the smooth and Kahler geometries as well as the world of low-dimensional topology. In the second part, I’ll discuss the symplectic Torelli group for higher dimensional symplectic manifolds, and an ongoing project to use Gromov-Witten theory to detect interesting elements. 10-23-2017 *Monday* Florian Beck, Universität Hamburg Hitchin systems in terms of Calabi-Yau threefolds. Abstract: Integrable systems are often constructed from geometric and/or Lie-theoretic data. Two important example classes are Hitchin systems and Calabi-Yau integrable systems. A Hitchin system is constructed from a compact Riemann surface  together with a complex Lie group with mild extra conditions. In contrast, Calabi-Yau integrable systems are constructed from a priori purely geometric data, namely certain families of Calabi-Yau threefolds. Despite their different origins there is a non-trivial relation between Hitchin and Calabi-Yau integrable systems. More precisely, we will see in this talk that any Hitchin system for a simply-connected or adjoint simple complex Lie group is isomorphicto a Calabi-Yau integrable system (away from singular fibers). 11-01-2017 *12:30pm-1:30pm* Chenglong Yu, Harvard Math Picard-Fuchs systems of zero loci of vector bundle sections Abstract: We propose an explicit construction for Picard-Fuchs systems of zero loci of vector bundle sections.  When the vector bundle admits large symmetry, the system we constructed is holonomic. This is a joint work with Huang, Lian and Yau. 11-06-2017 *Monday* Pietro Benetti Genolini (Univ. of Oxford) Topological AdS/CFT Abstract: I will describe a holographic dual to the Donaldson-Witten topological twist of gauge theories on a Riemannian four-manifold. Specifically, I will consider asymptotically locally hyperbolic solutions to Romans’ gauged supergravity in five dimensions with the four-manifold as conformal boundary, and show that the renormalised supergravity action is independent of the choice of boundary metric. This is a first step in the direction of combining topological quantum field theory with the AdS/CFT correspondence. 11-13-2017 *Monday 12:30pm* *Room G02* Yusuf Baris Kartal (MIT) Dynamical invariants of categories associated to mapping tori Abstract: One can construct the symplectic mapping torus for a given a symplectic manifold with a symplectomorphism and use the flux invariant to distinguish the mapping tori of maps of different order. The essential argument is that the flow in a certain direction have different periods depending on the order of the symplectomorphism. In this talk, we will introduce an abstract categorical version of the mapping torus- associated to an $A_\infty$ category and an auto-equivalence. Then, we will construct a family of bimodules analogous to the flow and discuss how to characterize it intrinsically and how to use it to distinguish different categorical mapping tori. 11-22-2017 No Talk 11-29-2017 Amitai Zernik (IAS) Computing the A∞ algebra of RP2m ↪ CP2m using open fixed-point localization. Abstract: I’ll explain how to compute the equivariant quantum A∞ algebra A associated with the Lagrangian embedding of RP2m in CP2m, using a new fixed-point localization technique that takes into account contributions from all the corner strata. It turns out that A is rigid, so its structure constants are independent of all choices. When m = 1 and in the non-equivariant limit, they specialize to give Welschinger’s counts of real rational planar curves passing through some generic, conjugation invariant congurations of points in CP2m. So we get a diagrammatic expression for computing Welschinger invariants, which I’ll demonstrate with some examples.Time permitting, I’ll discuss a formal extension to higher genus which satises string and dilaton. 12-06-2017 Sarah Venkatesh (Columbia) Closed-string mirror symmetry for subdomains Abstract: We construct a symplectic cohomology theory for Liouville cobordisms that detects non-trivial elements of the Fukaya category.  This theory is conjecturally mirror to the Jacobian ring of a Landau-Ginzburg superpotential on an affinoid subdomain.  We illustrate this manifestation of mirror symmetry by examining cobordisms contained in negative line bundles.