# Joint IAS-PU Symplectic Geometry Seminar

## Relative quantum product and open WDVV equations

Sara Tukachinsky
University of Montreal
February 2, 2017
The standard WDVV equations are PDEs in the potential function that generates Gromov-Witten invariants. These equations imply relations on the invariants, and sometimes allow computations thereof, as demonstrated by Kontsevich-Manin (1994). We prove analogous equations for open Gromov-Witten invariants that we defined in a previous work. For ($\mathbb CP^n$ ,$\mathbb RP^n$), the resulting relations allow the computation of all invariants. The formulation of the open WDVV requires a lift of the big quantum product to relative cohomology.

## $C^0$ Hamiltonian dynamics and a counterexample to the Arnold conjecture

Member, School of Mathematics
November 29, 2016
After introducing Hamiltonian homeomorphisms and recalling some of their properties, I will focus on fixed point theory for this class of homeomorphisms. The main goal of this talk is to present the outlines of a $C^0$ counterexample to the Arnold conjecture in dimensions four and higher. This is joint work with Lev Buhovsky and Vincent Humiliere.

## Rectification and the Floer complex: quantizing Lagrangians in $T^*N$

Claude Viterbo
Ecole Normale Supérieure
November 29, 2016
We shall give a construction of the quantized sheaf of a Lagrangian submanifold in $T^*N$ and explain a number of features and applications.

## The gauged symplectic sigma-model

Constantin Teleman
University of California, Berkeley and Oxford University
November 15, 2016
I will recall the construction of the space of states in a gauged topological A-model. Conjecturally, this gives the quantum cohomology of Fano symplectic quotients: in the toric case, this is Batyrev’s presentation of quantum cohomology of toric varieties. Time permitting, I will discuss the role of “Coulomb branches” in gauge theory in relation to equivariant quantum and symplectic cohomology.

## Monotone Lagrangians in cotangent bundles

Luis Diogo
Columbia University
October 11, 2016
We show that there is a 1-parameter family of monotone Lagrangian tori in the cotangent bundle of the 3-sphere with the following property: every compact orientable monotone Lagrangian with non-trivial Floer cohomology is not Hamiltonian-displaceable from either the zero-section or one of the tori in the family. The proof involves studying a version of the wrapped Fukaya category of the cotangent bundle which includes monotone Lagrangians. Time permitting, we may also discuss an extension to other cotangent bundles. This is joint work with Mohammed Abouzaid.