Geometry and Physics Seminar

During the summer of 2020, the CMSA will be hosting a new Geometry Seminar. Talks will be scheduled on Mondays at 9:30pm or Tuesdays at 9:30am, depending on the location of the speaker. This seminar is organized by Tsung-Ju Lee, Yoosik Kim, and Du Pei.

To learn how to attend this seminar, please fill out this form

You can contact the organizers by emailing: tjlee@cmsa.fas.harvard.edu.

DateSpeakerTitle/Abstract
6/2/2020
9:30am ET
Siu-Cheong Lau
Boston University
This meeting will be taking place virtually on Zoom.

Speaker: Equivariant Floer theory and SYZ mirror symmetry

Abstract: In this talk, we will first review a symplectic realization of the SYZ program and some of its applications. Then I will explain some recent works on equivariant Lagrangian Floer theory and disc potentials of immersed SYZ fibers. They are joint works with Hansol Hong, Yoosik Kim and Xiao Zheng.
6/8/2020
9:30pm ET
Youngjin Bae (KIAS)This meeting will be taking place virtually on Zoom.

Title: Legendrian graphs and their invariants

Abstract: Legendrian graphs naturally appear in the study of Weinstein manifolds with a singular Lagrangian skeleton, and a tangle decomposition of Legendrian submanifolds. I will introduce various invariant of Legendrian graphs including DGA type, polynomial type, sheaf theoretic one, and their relationship. This is joint work with Byunghee An, and partially with Tamas Kalman and Tao Su.
6/16/2020
9:30am ET
Michael McBreen (CMSA)This meeting will be taking place virtually on Zoom.

Title: Loops in hypertoric varieties and symplectic duality

Abstract: Hypertoric varieties are algebraic symplectic varieties associated to graphs, or more generally certain hyperplane arrangements. They make many appearances in modern geometric representation theory. I will discuss certain infinite dimensional or infinite type generalizations of hypertoric varieties which occur in the study of enumerative invariants, focusing on some elementary examples. Joint work with Artan Sheshmani and Shing-Tung Yau.
6/22/2020
9:30pm ET
Ziming Ma (CUHK)This meeting will be taking place virtually on Zoom.

Title: The geometry of Maurer–Cartan equation near degenerate Calabi–Yau varieties

Abstract: In this talk, we construct a dgBV algebra PV*(X) associated to a possibly degenerate Calabi–Yau variety X equipped with local thickening data. This gives a version of the Kodaira–Spencer dgLa which is applicable to degenerated spaces including both log smooth or maximally degenerated Calabi–Yau. We use this to prove an unobstructedness result about the smoothing of degenerated Log Calabi–Yau varieties X satisfying Hodge–deRham degeneracy property for cohomology of X, in the spirit of Kontsevich–Katzarkov–Pantev. This is a joint work with Kwokwai Chan and Naichung Conan Leung.
6/30/2020
9:30pm ET
Sunghyuk Park (Caltech)This meeting will be taking place virtually on Zoom.

Title: 3-manifolds, q-series, and topological strings

Abstract: \hat{Z} is an invariant of 3-manifolds valued in q-series (i.e. power series in q with integer coefficients), which has interesting modular properties. While originally from physics, this invariant has been mathematically constructed for a big class of 3-manifolds, and conjecturally it can be extended to all 3-manifolds. In this talk, I will give a gentle introduction to \hat{Z} and what is known about it, as well as highlighting some recent developments, including the use of R-matrix, generalization to higher rank, large N-limit and interpretation as open topological string partition functions. 
7/7/2020
9:30am ET
Jeremy Lane  (McMaster University)This meeting will be taking place virtually on Zoom.

Title: Collective integrable systems and global action-angle coordinates


Abstract: A “collective integrable system” on a symplectic manifold is a commutative integrable system constructed from a Hamiltonian action of a non-commutative Lie group. Motivated by the example of Gelfand-Zeitlin systems, we give a construction of collective integrable systems that generate a Hamiltonian torus action on a dense subset of any Hamiltonian K-manifold, where K is any compact connected Lie group. In the case where the Hamiltonian K-manifold is compact and multiplicity free, the resulting Hamiltonian torus action is completely integrable and yields global action angle coordinates.  Moreover, the image of the moment map is a (non-simple) convex polytope. 

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