Video Lectures

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...

How and where do black hole mergers form in our Universe? After 10 years of GW science with LIGO/Virgo/Kagra, there still seems to be no direct indication of what the underlying astrophysical formation channels are. I will present ideas and ongoing...

Inspired by the Erdos--Renyi model for random graphs, Linial and Meshulam devised in 2006 a model for random 2-dimensional simplicial complexes. The goal of this talk (and the next) is to present some nice results about the behavior of these random...

This talk is concerned with solutions of the 3D incompressible Navier-Stokes equations that are bounded in a critical space. From small initial data, these solutions are known to be globally well-posed due to classical work of Fujita-Kato and others...

The compressible Euler equation can lead to the emergence of shock discontinuities in finite time, notably observed behind supersonic planes. A very natural way to justify these singularities involves studying solutions as inviscid limits of Navier...