Prof Gérard Ben Arous (TheCourant Institute of Mathematical Sciences at New York University)

The Elastic Manifold is a model of elastic interface in a disordered medium, introduced in the 80’s in order to understand the competition between the effects of disorder and those of elasticity. This model gave us a vast literature in statistical physics, inspired by the progress of the Parisi school on Spin Glasses, up to the more mathematical recent works by Fyodorov and Le Doussal.
I will cover here recent progress, first on the topological complexity of the energy  landscape for the Elastic Manifold ( recently obtained with Paul Bourgade (Courant) and Ben McKenna (Harvard)), and then on the Parisi formula for the quenched free energy, and the nature of the glassy transition at low temperature (more recently proved in a series of works to be posted, with Pax Kivimae (Courant).