Joint IAS-PU Symplectic Geometry Seminar

In this talk, I would like to explain my joint work with Weiwei Wu about understanding projective Dehn twist using Lagrangian cobordism.

This is a part of my joint work with Oh-Ohta-Ono and is a part of project to rewrite the whole story of virtual fundamental chain in a way easier to use. In general we can construct virtual fundamental chain on (basically all) the moduli space of...

Joint work with Ivan Smith. Let p be a positive integer. Take the quotient of a 2-disc by the equivalence relation which identifies two boundary points if the boundary arc connecting them subtends an angle which is an integer multiple of ($2 \pi / p...

The dichotomy between overtwisted and tight contact structures has been central to the classification of contact structures in dimension 3. Ozsvath-Szabo's contact invariant in Heegaard Floer homology proved to be an efficient tool to distinguish...

McDuff and Schlenk studied an embedding capacity function, which describes when a 4-dimensional ellipsoid can symplectically embed into a 4-ball. The graph of this function includes an infinite staircase determined by the odd index Fibonacci numbers...

We present several classification results for Lagrangian tori, all proven using the splitting construction from symplectic field theory. Notably, we classify Lagrangian tori in the symplectic vector space up to Hamiltonian isotopy; they are either...

I'll outline recent results with Steven Sivek classifying the Stein fillings, up to topological homotopy equivalence, of the canonical contact structure on the unit cotangent bundle of a surface. The proof begins with Li, Mak and Yasui's technology...

After recalling some recent developments in symplectic flexibility, I will introduce a class of open symplectic manifolds, called "subflexible", which are not flexible but become so after attaching some Weinstein handles. For example, the standard...

In 2000 Eliashberg-Polterovich introduced the concept of positivity in contact geometry. The notion of a positive loop of contactomorphisms is central. A question of Eliashberg-Polterovich is whether $C^0$-small positive loops exist. We give a...

I will describe a formalism for (Lagrangian) Floer theory wherein the output is not a deformation of the cohomology ring, but of the Pontryagin algebra of based loops, or of the analogous algebra of based discs (with boundary on the Lagrangian). I...