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Gerard Ben Arous, New York University
September 21, 2023 @ 5:00 pm - 6:00 pm UTC+4
Title: “The topological complexity and free energy of the Elastic Manifold”
Abstract:
“The Elastic Manifold is a complex and central model of a random interface in quenched disorder. Its behavior has been extensively studied in Physics, since the initial study by Mézard and Parisi in the 90’s, and until the recent work by Fyodorov-Le Doussal.
I will survey recent mathematical results with Paul Bourgade and Benjamin McKenna on the annealed topological complexity of this interface, which relies on delicate Random Matrix Theory results. If time permits, I will give even more recent results with Pax Kivimae on the quenched free energy, which confirm the Mézard-Parisi prediction that the phase boundary for the Replica Symmetry Breaking region is given by the so-called Larkin mass.”