Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

I will motivate the study of coproducts and describe a new coproduct structure on the symplectic cohomology of Liouville manifolds. Time permitting, I will indicate how to compute it in an example to show that it's not trivial. This is based on my...

I will discuss how the Deligne-Mumford compactification of curves arises from the uncompactified moduli spaces of curves as a result of some algebraic operations related to (pr)operadic structures on the moduli spaces. I will describe how a...

We present recent developments in symplectic geometry and explain how they motivated new results in the study of cluster algebras. First, we introduce a geometric problem: the study of Lagrangian surfaces in the standard symplectic 4-ball bounding...

We introduce new invariants to the existence of Lagrangian

cobordisms in R^4. These are obtained by studying holomorphic disks

with corners on Lagrangian tangles, which are Lagrangian cobordisms

with flat, immersed boundaries.

We develop...

Persistence modules and barcodes are used in symplectic topology to define new invariants of Hamiltonian diffeomorphisms, however methods that explicitly calculate these barcodes are often unclear. In this talk I will define one such invariant...

The ellipsoidal embedding function of a symplectic four manifold M measures how much the symplectic form on M must be dilated in order for it to admit an embedded ellipsoid of some eccentricity. It generalizes the Gromov width and ball packing...

The spectral norm provides a lower bound to the Hofer norm. It is thus natural to ask whether the diameter of the spectral norm is finite or not. During this short talk, I will give a sketch of the proof that, in the case of Liouville domains, the...

I will explain how to construct the Ruelle invariant of a symplectic cocycle over an arbitrary measure preserving flow. I will provide examples and computations in the case of Hamiltonian flows and Reeb flows (in particular, for toric domains). As...

Relative symplectic cohomology is a Floer theoretic invariant associated with compact subsets K of a closed or geometrically bounded symplectic manifold M. The motivation for studying it is that it is often possible to reduce the study of global...

Gromov-Witten invariants for a general target are rational-valued but not necessarily integer-valued. This is due to the contribution of curves with nontrivial automorphism groups. In 1997 Fukaya and Ono proposed a new method in symplectic geometry...