Joint IAS-PU Symplectic Geometry Seminar

Abstract: In this talk, I will give a new construction of the Morse-Bott cochain complex, where the underlying vector space is generated by the cohomology of the critical manifolds. This new construction has two nice features: (1) It requires the...

Inspired by homological mirror symmetry for non-compact manifolds, one wonders what functorial properties wrapped Fukaya categories have as mirror to those for the derived categories of the mirror varieties, and also whether homological mirror...

Consider a Lagrangian torus fibration a la SYZ over a non compact base. Using techniques from arXiv:1510.04265, I will discuss the construction of wrapped Floer theory in this setting. Note that this setting is generally not exact even near infinity...

I will report on joint work with Andrew Lee, which explores the notion that spaces of stable pairs over Riemann surfaces (in the sense of Bradlow and Thaddeus) could form a natural home for a “non-abelian” analog of Heegaard Floer homology for 3...

Given a fibration of compact symplectic manifolds and an induced fibration of Lagrangians, one can ask if we can compute the Floer cohomology of the total Lagrangian from information about the base and fiber Lagrangians. The primary example that we...

Motivated by the goal of establishing a "symplectic sum formula" in symplectic field theory, we will discuss the intersection behavior between punctured pseudoholomorphic curves and symplectic hypersurfaces in a symplectization. In particular we...

In this talk, following right after Chiu's, I will summarize two other tools capable of detecting the non-squeezing property of pre-quantized balls in $\mathbb R^{2n} \times S^1$. One of these is a $\mathbb Z_k$-equivariant version of contact...

In this talk I will introduce a way to associate a triangulated category of sheaves with a domain of $\mathbb R^{2n} \times S^1$. The cohomological information on the category side helps to detect the contact non-squeezing property of the domain on...

The group $\mathrm{SL}_n(\mathbb Z)$ (when $n > 2$) is very rigid, for example, Margulis proved all its linear representations come from representations of $\mathrm{SL}_n(\mathbb R)$ and are as simple as one can imagine. Zimmer's conjecture states...

I will explain the main ideas of a proof that for generic compatible almost complex structures in symplectic manifolds of dimension at least 6, closed embedded J-holomorphic curves of index 0 are always "super-rigid", implying that their multiple...