Video Lectures

I will discuss a recursive formula for the homotopy type of the space of Legendrian embeddings of sufficiently positive cables with the maximal Thurston-Bennequin invariant. Via this formula, we identify infinitely many new components within the...

Lagrangian cobordisms induce exact triangles in the Fukaya category. But how many exact triangles can be recovered by Lagrangian cobordisms? One way to measure this is by comparing the Lagrangian cobordism group to the Grothendieck group of the...

In the talk, I will introduce a distance-like function on the zero section of the cotangent bundle using symplectic embeddings of standard balls inside an open neighborhood of the zero section. I will provide some examples which illustrate the...

Given a lagrangian link with k components it is possible to define an associated Hofer norm on the braid group with k strands. In this talk we are going to detail this definition, and explain how it is possible to prove non degeneracy if k=2 and...

Floer homotopy type refines the Floer homology by associating a (stable) homotopy type to an Hamiltonian, whose homology gives the Hamiltonian Floer homology. In particular, one expects the existing structures on the latter to lift as well, such as...

We consider 2D quantum materials (non-magnetic and constant magnetic field cases), modeled by a continuum Schroedinger operator, whose potential is a sum of translates of an atomic well, centered on the vertices of a discrete subset of the plane...

I will discuss how to build small symplectic caps for contact manifolds as a step in building small closed symplectic 4-manifolds. As an application of the construction, I will give explicit handlebody descriptions of symplectic embeddings of...

I consider the operator product algebra along an observer's worldline as a background independent algebra in quantum gravity.

We introduce a framework for quantifying random matrix behavior of 2d CFTs and AdS3 quantum gravity. This is anchored by a 2d CFT trace formula, analogous to the Gutzwiller trace formula for chaotic quantum systems. We use this framework to...

The Bekenstein bound posits a maximum entropy for matter with finite energy confined to a spacetime region. It is often interpreted as a fundamental limit on the information that can be stored by physical objects. In this work, we test this...