Topology and Symplectic Geometry / Math of Gauge Fields seminar

from Thursday
June 01, 2017 to Sunday
December 31, 2017
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Instructions for subscribing to Stony Brook Math Department Calendars

Thursday
September 07, 2017

1:00 PM - 2:00 PM
Math Tower 5-127
Kei Irie, RIMS, Kyoto University
Chain-level string topology, pseudo-holomorphic disks, and Kuranishi structures

I will talk about an application of chain-level string topology to pseudo-holomorphic curve theory in symplectic topology.
Specifically, for any closed, oriented and spin Lagrangian submanifold $L$ in a symplectic vector space,
one can define a Maurer-Cartan element of the loop bracket defined at chain level,
using virtual fundamental chain of the moduli space of pseudo-holomorphic disks with boundaries on $L$.
This idea is due to Fukaya, who also pointed out its important consequences in symplectic topology.

I will explain how to rigorously carry out this idea, using a novel chain model of the free loop space and the theory of Kuranishi structures.


Thursday
September 21, 2017

1:00 PM - 2:00 PM
5-127
Artem Kotelskiy, Princeton
Bordered theory for pillowcase homology.

Pillowcase homology is a geometric construction, which was developed in order to better understand and compute a knot invariant called singular instanton knot homology. We will describe an algebraic extension of pillowcase homology. We will compute partially wrapped Fukaya category of the pillowcase enlarged by immersed Lagrangians, and thus translate geometric pieces of pillowcase homology construction into algebraic world. The main ingredient will be a certain type DD structure, which allows one to recover Lagrangian Floer homology from modules in a computable and geometrically clear way.


Thursday
October 05, 2017

1:00 PM - 2:00 PM
5-127
Umut Varolgunes, MIT
Mayer-Vietoris sequence for relative symplectic cohomology

I will first recall the definition of an invariant that assigns to any compact subset K of a closed symplectic manifold M a module SH_M(K) over the Novikov ring. I will go over the case of M=two sphere to illustrate various points about the invariant. Finally I will state the Mayer-Vietoris property and explain under what conditions it holds.


Thursday
October 12, 2017

1:00 PM - 2:00 PM
MAT 5-127
Mohammad Tehrani, Stony Brook University
Compactification of moduli spaces of J-holomorphic maps relative to snc divisors

In this talk, I will describe an efficient way of compactifying moduli space of J-holomorphic maps relative to simple normal crossings (snc) symplectic divisors, including the holomorphic case. The primary goal of this construction is to define Gromov-Witten invariants relative to snc divisors, and to establish a GW-degeneration formula for any semistable degeneration with an snc central fiber.


Thursday
October 19, 2017

1:00 PM - 2:00 PM
MAT 5-127
Chris Scaduto, Stony Brook University
An odd Khovanov homotopy type

Associated to a link, Lipshitz and Sarkar constructed a refinement of Khovanov homology that takes the form of a stable homotopy type. I'll explain how to construct similar refinements for other versions of Khovanov homology, including the "odd" theory, and take some time to explain some motivations from mathematical gauge theory. This is joint work with S. Sarkar and M. Stoffregen.


Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars