# MSRI Moduli and Representation Theory Seminar, Spring 2018.

Location: MSRI, Baker room
Time: Monday 3:30-4:30
Organizers: Andrei Neguț, Georg Oberdieck, ...

Feb 1:   Hyenho Lho (ETH Zurich), Holomorphic anomaly equation for local P2, [C3/Z3], formal quintic
Feb 11:   Eugene Gorsky (UC Davis), Khovanov-Rozansky homology and Hilbert schemes of points
Feb 21, 1.30-2.30:   Nora Ganter (University of Melbourne), The Geometry of equivariant elliptic cohomology
Feb 26:   Matthew Krauel (California State University, Sacramento), Jacobi forms, differential operators, and vertex operator algebras
Mar 5:   Katrin Wehrheim (UC Berkeley), Pseudoholomorphic Quilts and higher categorical structures in symplectic topology
Mar 12:   Andrey Smirnov (UC Berkeley), Elliptic stable envelope for Hilbert scheme of points on C^2
Mar 19:   Workshop week, no talk.
Mar 26:   Nate Bottman (IAS), Quilted disks and functors between Fukaya categories
Apr 2:   Michail Savvas (Stanford University), Generalized Donaldson-Thomas Invariants via Kirwan Blowups
Apr 9: (no seminar)
Apr 16:   Erik Carlsson (University of California, Davis), Diagonal coinvariants and affine Schubert calculus
Apr 23:   Sheldon Katz (University of Illinois at Urbana-Champaign), Refined BPS invariants for local del Pezzos and representations of affine E_8
Apr 30: (no seminar)
May 7:   Felix Janda (University of Michigan), On Gromov-Witten theory of hypersurfaces
May 14: (no seminar)
May 21:   Kai Behrend (University of British Columbia), dg-manifolds form a category of fibrant objects
May 23:   Max Zimet (Stanford University), BPS State Counts in 4d N=4 String Theory, with Applications to Moonshine

Abstracts:

Feb 1. Hyenho Lho. I will discuss the holomorphic anomaly equation for GW invariants of several Calabi-Yau geometries. Holomorphic anomaly equation was originated from Physics B-model which recursively determine higher genus GW invariants in terms of lower genus invariants. I will explain how one can study holomorphic anomaly equation in mathematics for several examples. This talk is based on joint work with Rahul Pandharipande.

Feb 11. Eugene Gorsky. Khovanov and Rozansky introduced a link homology theory which categorifies the HOMFLY polynomial. This invariant has a lot of interesting properties, but it is notoriously hard to compute. I will introduce HOMFLY homology and discuss its conjectural relation to algebraic geometry of the Hilbert scheme of points on the plane. In particular, I will compute this invariant for all positive powers of the full twist and match it to the family of ideals appearing in Haiman's description of the isospectral Hilbert scheme. The talk is based on joint works with Matt Hogancamp, Andrei Negut and Jacob Rasmussen.

Feb 21. Nora Ganter. I will give an introduction to the construction of equivariant elliptic cohomology and then talk about some recent geometric approaches to the subject.

Feb 26. Matthew Krauel. We will briefly explain how differential operators of Jacobi forms arise in the theory of vertex operator algebras (VOAs). We then introduce a family of differential operators that arise for a certain class of VOAs and explain some possible applications. Time permitting, we will also mention how the theory of VOAs can be used to show how certain polynomials of quasi-Jacobi forms are Jacobi forms.

Mar 5. Katrin Wehrheim. Starting from string diagrams for 2-categories, I will introduce the basic approach of my joint works (in progress) with Bottman / Ma'u / Woodward: Translate string diagrams into moduli spaces of pseudoholomorphic quilts, prove the algebraic axioms by adiabatic analysis, and get 2-categorical structures. In particular, this associates to any Lagrangian relation L\subset M \times N a functor Fuk(M) \to Fuk(N) between (some version of) Fukaya categories. (Depending on the symplectic manifolds, this is a result with Ma'u-Woodward or work in progress with Bottman.)