Video Lectures

Supermassive black hole mergers are extraordinary cosmic phenomena characterized by their immense energy release, producing gravitational waves that can rival the total light output of all stars in the universe within a short time frame. These...

I will review the Penrose and Wall singularity theorems and describe their limitations. Following Shahbazi-Moghaddam, I will argue that semiclassical gravity in the infinite species limit becomes an exact theory whose metric is defined on all scales...

Not much is known about what happens at the end of black hole evaporation. Pushing the semi-classical evolution well beyond its regime of validity suggests that the final Cauchy slice breaks into a piece that remains behind the event horizon...

Last week we defined the Linial--Meshulam model for random 2 dimensional simplicial complexes and discussed two notions of connectivity for it: Vanishing of its 1st cohomology with F2 coefficients, and vanishing of its fundamental group. This time...

In this talk, I will explore the fascinating landscape of assumptions in quantum cryptography—especially, how little we need to assume to build secure quantum protocols. We will cover key cryptographic primitives including quantum encryption...

Given a Morse-Smale pair on a manifold M, it is possible to entirely recover its fundamental group in a combinatorial manner. We call this construction the Morse fundamental group. Motivated by a similar construction of a « Floer fundamental group »...

Lagrangian Floer theory is useful to detect non-displaceability of Lagrangian submanifolds via Hamiltonian isotopies. A related question, in the presence of a group action, is whether a certain Lagrangian is equivariantly displaceable, that is by a...

We compute the subleading asymptotics of the ECH and elementary ECH capacities of toric domains and show that they recover the perimeter in the liminf, without any genericity required.  As an application, we give the first examples of the failure of...

Remarkable martensitic microstructures are observed in the alloy  Ti76Nb22Al2 , which undergoes a cubic to orthorhombic transformation with six martensitic variants Ui=UTi greater than 0 having middle eigenvalue λ2(Ui) very close to 1. Assuming that...