Thursday January 25, 2018 1:00 PM  2:00 PM MAT 5127
 Kenji Fukaya, Stony Brook University
Gluing analysis in relative Gromov Witten theoryIn this talk, I will explain certain points about the construction of Kuranishi structure (or anything similar to obtain virtual fundamental chains) on the compactification of moduli spaces appearing in relative GromovWitten theory and their variants in Floer homology. Various points of the construction are similar to the case of stable map compactification for ordinary Gromov Witten theory. However, there are certain points which are not discussed in the literature and are not so much trivial.

Thursday February 01, 2018 1:00 PM  2:00 PM MAT 5127
 Linh Truong, Columbia University
Truncated Heegaard Floer homology and concordance invariantsHeegaard Floer homology has proven to be a useful tool in the study of knot concordance. Ozsvath and Szabo first constructed the tau invariant using the hat version of Heegaard Floer homology and showed tau provides a lower bound on the slice genus. Later, Hom and Wu constructed a concordance invariant using the plus version of Heegaard Floer homology; this provides an even better lowerbound on the slice genus. In this talk, I discuss a sequence of concordance invariants that are derived from the truncated version of Heegaard Floer homology. These truncated Floer concordance invariants generalize the OzsvathSzabo and HomWu invariants.

Thursday April 26, 2018 1:00 PM  2:00 PM MAT 5127
 Sara Venkatesh, Columbia University
Quantitative symplectic cohomology
Quantitative symplectic cohomologyMirror symmetry predicts the existence of Floer invariants that yield “local” information about the Fukaya category. Guided by this, we construct a quantitative symplectic cohomology theory that detects Floeressential Lagrangians within subdomains. This theory conjecturally specializes to a flavor of Rabinowitz Floer homology. We illustrate the quantitative behavior of this theory by examining negative line bundles over toric symplectic manifolds.

Thursday May 03, 2018 1:00 PM  2:00 PM MAT 5127
 Michael Miller, UCLA
Equivariant instanton homology and group cohomologyFloer's celebrated instanton homology groups are defined for integer homology spheres, but analagous groups in Heegaard Floer and Monopole Floer homology theories are defined for all 3manifolds; these latter groups furthermore come in four flavors, and carry extra algebraic structure. Any attempt to extend instanton homology to a larger class of 3manifolds must be somehow equivariant  respecting a certain SO(3)action. We explain how ideas from group cohomology and algebraic topology allow us to define four flavors of instanton homology for rational homology spheres, and how these invariants relate to existing instanton homology theories.

Thursday May 10, 2018 1:00 PM  2:00 PM SCGP 313
 Guangbo Xu, Princeton
BershadskyCecottiOoguriVafa torsion in LandauGinzburg modelsIn the celebrated work of BershadskyCecottiOoguriVafa the genus one string amplitude in the Bmodel is identified with certain analytic torsion of the Hodge Laplacian on a Kähler manifold. In a joint work with Shu Shen (IMJPRG) and Jianqing Yu (USTC) we study the analogous torsion in LandauGinzburg models. I will explain the corresponding index theorem based on the asymptotic expansion of the heat kernel of the Schrödinger operator. I will also explain the rigorous definition of the BCOV torsion for homogeneous polynomials on ${\mathbb C}^N$. Lastly I will explain the conjecture stating that in the CalabiYau case the BCOV torsion solves the holomorphic anomaly equation for marginal deformations.

Thursday May 24, 2018 1:00 PM  2:00 PM MAT 5127
 Andrew Hanlon, UC Berkeley
Categorical monodromy for mirrors of toric varietiesWe will discuss a monodromy action on the FukayaSeidel category of a Laurent polynomial from varying the arguments of the polynomial's coefficients. We will see how this monodromy corresponds under homological mirror symmetry to tensoring by a line bundle naturally associated to the monomials whose coefficients are rotated. This will require a new interpretation of the FukayaSeidel category in this setting.

