## Continuous covers on symplectic manifolds

François Lalonde

University of Montreal

March 24, 2017

François Lalonde

University of Montreal

March 24, 2017

Daniel Alvarez-Gavela

Stanford University

March 23, 2017

Chris Woodward

Rutgers University

March 9, 2017

I hope to talk more about how to find generators for Fukaya categories using symplectic version of the minimal model program in examples such as symplectic quotients of products of spheres and moduli spaces of parabolic bundles.

Alexandru Oancea

Université Pierre et Marie Curie; Member, School of Mathematics

February 23, 2017

Symplectic homology for a Liouville cobordism (possibly filled at the negative end) generalizes simultaneously the symplectic homology of Liouville domains and the Rabinowitz-Floer homology of their boundaries. I intend to explain a conceptual framework within which one can understand it, and give a sample application which shows how it can be used in order to obstruct cobordisms between contact manifolds. Based on joint work with Kai Cieliebak and Peter Albers.

Kei Irie

Kyoto University

February 16, 2017

$C^r$ closing lemma is an important statement in the theory of dynamical systems, which implies that for a $C^r$ generic system the union of periodic orbits is dense in the nonwondering domain. $C^1$ closing lemma is proved in many classes of dynamical systems, however $C^r$ closing lemma with $r > 1$ is proved only for few cases. In this talk, I'll prove $C^\infty$ closing lemma for Reeb flows on closed contact three-manifolds. The proof uses recent developments in quantitative aspects of embedded contact homology (ECH).

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.

Sobhan Seyfaddini

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.

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.

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.

Ivan Smith

University of Cambridge

November 1, 2016

Let $n > 1$. Given two maps of an $n$-dimensional sphere into Euclidean $2n$-space with disjoint images, there is a $\mathbb Z/2$ valued linking number given by the homotopy class of the corresponding Gauss map. We prove, under some restrictions on $n$, that this vanishes when the components are immersed Lagrangian spheres each with exactly one double point of high Maslov index. This is joint work with Tobias Ekholm.