Joint IAS-PU Symplectic Geometry Seminar

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...

I will discuss some recent work (mostly joint with Dan Cristofaro-Gardiner and Richard Hind) on the stabilized symplectic embedding problem for ellipsoids into balls. The main tools come from embedded contact homology.

We look at the following chain of symplectic embedding problems in dimension four. \[E(1, a) \to Z_4(A),\ E(1, a) \to C_4(A),\ E(1, a) \to P(A, ba) (b \in {\mathbb N}_{\geq 2}),\ E(1, a) \to T_4(A).\] Here $E(1, a)$ is a symplectic ellipsoid, $Z_4(A...

In this talk, we first introduce the notion of a continuous cover of a manifold parametrised by any compact manifold endowed with a mass 1 volume-form. We prove that any such cover admits a partition of unity where the usual sum is replaced by...