Thursday September 07, 2017 1:00 PM  2:00 PM Math Tower 5127
 Kei Irie, RIMS, Kyoto University
Chainlevel string topology, pseudoholomorphic disks, and Kuranishi structures I will talk about an application of chainlevel string topology to pseudoholomorphic curve theory in symplectic topology.
Specifically, for any closed, oriented and spin Lagrangian submanifold $L$ in a symplectic vector space,
one can define a MaurerCartan element of the loop bracket defined at chain level,
using virtual fundamental chain of the moduli space of pseudoholomorphic 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 5127
 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 5127
 Umut Varolgunes, MIT
MayerVietoris sequence for relative symplectic cohomologyI 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 MayerVietoris property and explain under what conditions it holds.

Thursday October 12, 2017 1:00 PM  2:00 PM MAT 5127
 Mohammad Tehrani, Stony Brook University
Compactification of moduli spaces of Jholomorphic maps relative to snc divisorsIn this talk, I will describe an efficient way of compactifying moduli space of Jholomorphic maps relative to simple normal crossings (snc) symplectic divisors, including the holomorphic case. The primary goal of this construction is to define GromovWitten invariants relative to snc divisors, and to establish a GWdegeneration formula for any semistable degeneration with an snc central fiber.

Thursday October 19, 2017 1:00 PM  2:00 PM MAT 5127
 Chris Scaduto, Stony Brook University
An odd Khovanov homotopy typeAssociated 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.

