Topology and Symplectic Geometry / Math of Gauge Fields seminar

from Thursday
June 01, 2017 to Sunday
December 31, 2017
 Show events for: All Events AGNES Algebraic geometry seminar Algebraic models in geometry seminar Am.Math.Soc. (AMS) Chapter Seminar Analysis Seminar Analysis Seminar Analysis Student Seminar Capsule Research Talks Colloquium Commencement Ceremony Comprehensive Exams Dynamical Systems Seminar Equivalence Method and Exterior Differential Systems Seminar First and Second Year Student Seminar Friday Summer Meeting Geometric Analysis Learning Seminar Geometry/Topology Seminar Grad / Postdoc Professional Development Seminar Graduate Student Seminar Graduate Topology Seminar Grant Proposal Panel Hodge Theory, Moduli and Representation Theory Holiday Party Joint Columbia-CUNY-Stony Brook General Relativity Seminar Math Club Math Day 2016 Math in Jeans Mathematical Writing Seminar Mathematics Education Colloquium Mathematics Summer Camp Mini Course / Dynamics Learning Seminar Mini-School in Geometry Minicourse in Real Enumerative Geometry New Graduate Students NY General Relativity Seminar Postdoc Geometry/Dynamics Seminar Postdoc Seminar RTG Colloquium RTG Seminar RTG Student Geometry Seminar Seminar in Topology and Symplectic Geometry Seminar on algebraic structures in physics Simons Colloquium Simons Lectures Series Singular metrics and direct images Special Algebra / Algebraic Geometry Seminar Special Analysis Seminar Special Colloquium Special Geometry/Topology Seminar Special Lectures Special Seminar in Algebraic Geometry Special Topology Seminar Student Algebraic Geometry Seminar Student Gauge Theory Seminar Student Seminar on Differential Geometry and Analysis Summer Workshop in Topology and Geometry Symplectic Geometry Reading Seminar Symplectic Geometry Seminar Thesis Defense Topology and Symplectic Geometry / Math of Gauge Fields seminar Women in Mathematics Instructions for subscribing to Stony Brook Math Department Calendars

 ThursdaySeptember 07, 20171:00 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.

 ThursdaySeptember 21, 20171:00 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.

 ThursdayOctober 05, 20171:00 PM - 2:00 PM 5-127 Umut Varolgunes, MIT Mayer-Vietoris 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 Mayer-Vietoris property and explain under what conditions it holds.

 ThursdayOctober 12, 20171:00 PM - 2:00 PM MAT 5-127 Mohammad Tehrani, Stony Brook University Compactification of moduli spaces of J-holomorphic maps relative to snc divisorsIn 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.

 ThursdayOctober 19, 20171:00 PM - 2:00 PM MAT 5-127 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.

 ThursdayNovember 09, 20171:00 PM - 2:00 PM MAT 5-127 Siqi He, caltech The Extended Bogomolny Equations, Generalized Nahm Pole and SL(2,R) Higgs Bundle.We will discuss Witten's gauge theory approaches to Jones polynomial and Khovanov homology by counting solutions to some gauge theory equations with singular boundary conditions. When we reduce these equations to 3-dimensional, we call them the extended Bogomolny equations. We develop a Donaldson-Uhlenbeck-Yau type correspondence for the moduli space of the extended Bogomolny equations on Riemann surface Σ times R^+ with Nahm pole singularity at Σ × {0} and the Teichmuller component of the stable SL(2, R) Higgs bundle, this verifies a conjecture of Gaiotto and Witten. The proof is based on an observation that the extended Bogomolny equations can be reduced to a Kazdan-Warner type equation. We will also discuss a partial correspondence for solutions with knot singularities in this program, corresponding to the non-Teichmuller components in the moduli space of stable SL(2, R) Higgs bundles. This is joint work with Rafe Mazzeo.

 ThursdayNovember 16, 20171:00 PM - 2:00 PM MATH 5-127 Francesco Lin, Princeton Connected sums in Pin(2)-monopole Floer homology.While not much is known about the structure of the homology cobordism group, Pin(2)-symmetry in Seiberg-Witten theory seems to provide a promising direction to unveil many of its properties. In this talk, we discuss the behavior under connected sums of the Floer theoretic invariants arising from it - and discuss possible applications.

 ThursdayNovember 30, 20171:00 PM - 2:00 PM MAT 5-127 Dingyu Yang, IAS Integral virtual fundamental chainsTo define invariants using moduli spaces of holomorphic curves in general symplectic manifolds, a virtual technique is typically required, such as Kuranishi theory or polyfolds. All the methods in full generality use perturbation or duality, involve locally breaking the symmetry then taking the weighted averages, and thus yield virtual fundamental chains over rationals. We carry out a program of Fukaya-Ono outlined in their 2001 paper. The key notions are a group-normal structure that one can always construct for a good coordinate system, and a group-normal complex structure that is always present on the moduli space of holomorphic curves, and their combined group-normal complex good coordinate system. Using this, one can perform a single-valued group-normally polynomial perturbation to yield integral virtual fundamental chains/pseudocycles for Floer/GW moduli spaces on general symplectic manifolds. This method is expected to be applicable to all moduli spaces based on holomorphic curves. This is a joint work with Guangbo Xu.

 ThursdayDecember 07, 20171:00 PM - 2:00 PM SCGP 103 Erkao Bao, Stony Brook University Semi-global Kuranishi charts and contact homologyContact homology was proposed and studied by Eliashberg, Givental and Hofer 16 years ago. It is a very powerful tool to distinguish different contact structures. However, the rigorous definition did not come out until 2015. In this talk, we will first see that the naive definition does not work because the moduli spaces of J-holomorphic curves that we count to define the differential of contact homology are not transversely cut out. In order to achieve transversality, we will use a simplified version of the FOOO's Kuranishi perturbation theory, consisting of "semi-global Kuranishi charts". This is a joint work with Ko Honda.

 Show events for: All Events AGNES Algebraic geometry seminar Algebraic models in geometry seminar Am.Math.Soc. (AMS) Chapter Seminar Analysis Seminar Analysis Seminar Analysis Student Seminar Capsule Research Talks Colloquium Commencement Ceremony Comprehensive Exams Dynamical Systems Seminar Equivalence Method and Exterior Differential Systems Seminar First and Second Year Student Seminar Friday Summer Meeting Geometric Analysis Learning Seminar Geometry/Topology Seminar Grad / Postdoc Professional Development Seminar Graduate Student Seminar Graduate Topology Seminar Grant Proposal Panel Hodge Theory, Moduli and Representation Theory Holiday Party Joint Columbia-CUNY-Stony Brook General Relativity Seminar Math Club Math Day 2016 Math in Jeans Mathematical Writing Seminar Mathematics Education Colloquium Mathematics Summer Camp Mini Course / Dynamics Learning Seminar Mini-School in Geometry Minicourse in Real Enumerative Geometry New Graduate Students NY General Relativity Seminar Postdoc Geometry/Dynamics Seminar Postdoc Seminar RTG Colloquium RTG Seminar RTG Student Geometry Seminar Seminar in Topology and Symplectic Geometry Seminar on algebraic structures in physics Simons Colloquium Simons Lectures Series Singular metrics and direct images Special Algebra / Algebraic Geometry Seminar Special Analysis Seminar Special Colloquium Special Geometry/Topology Seminar Special Lectures Special Seminar in Algebraic Geometry Special Topology Seminar Student Algebraic Geometry Seminar Student Gauge Theory Seminar Student Seminar on Differential Geometry and Analysis Summer Workshop in Topology and Geometry Symplectic Geometry Reading Seminar Symplectic Geometry Seminar Thesis Defense Topology and Symplectic Geometry / Math of Gauge Fields seminar Women in Mathematics Instructions for subscribing to Stony Brook Math Department Calendars