# Symplectic Dynamics/Geometry Seminar

### Packing and squeezing Lagrangian tori

We will ask how many Lagrangian tori, say with an integral area class, can be packed' into a given symplectic manifold. Similarly, given an arrangement of such tori, like the integral product tori in Euclidean space, one can ask about the...

### Classification of n-component links with Khovanov homology of rank 2^n

Boyu Zhang
Suppose L is a link with n components and the rank of Kh(L;Z/2) is 2^n, we show that L can be obtained by disjoint unions and connected sums of Hopf links and unknots. This result gives a positive answer to a question asked by Batson-Seed, and...

Aleksander Doan

Vinicius Ramos

### Local rigidity and C^0 symplectic and contact topology

Mike Usher

I will explain how coisotropic submanifolds of symplectic manifolds can be distinguished among all submanifolds by a criterion ("local rigidity") related to the Hofer energy necessary to disjoin open sets from them. This criterion is invariant under...

### Spectrum and abnormals in sub-Riemannian geometry: the 4D quasi-contact case

Nikhil Savale

We prove several relations between spectrum and dynamics including wave trace expansion, sharp/improved Weyl laws, propagation of singularities and quantum ergodicity for the sub-Riemannian (sR) Laplacian in the four dimensional quasi-contact case...

### Inscribing Rectangles in Jordan Loops

Rich Schwartz

I'll show a graphical user interface I wrote which explores the problem of inscribing rectangles in Jordan loops. The motivation behind this is the notorious Square Peg Conjecture of Toeplitz, from 1911.

I did not manage to solve this problem, but I...

### Bourgeois contact structures: tightness, fillability and applications.

Agustin Moreno
Starting from a contact manifold and a supporting open book decomposition, an explicit construction by Bourgeois provides a contact structure in the product of the original manifold with the two-torus. In this talk, we will discuss recent results...

### Constructions in symplectic and contact topology via h-principles

Oleg Lazarev

Certain flexible' structures in symplectic and contact topology satisfy h-principles, meaning that their geometry reduces to underlying topological data. Although these flexible structures have no interesting geometry by themselves, I will show how...

### The Arnold conjecture via Symplectic Field Theory polyfolds

Ben Filippenko

I will explain a polyfold proof, joint with Katrin Wehrheim, of the Arnold conjecture: the number of 1-periodic orbits of a nondegenerate 1-periodic Hamiltonian on a closed symplectic manifold is at least the sum of the Betti numbers. Our proof is a...