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Random tensors and random matrices in physics and mathematics.

Le : 22/04/2014 11h00
Par : Vietn Ahn NGUYEN
Lieu : I 103
Lien web :
Résumé : Quantum gravity is a grand effort to unify the two pillars of modern physics, quantum mechanics and general relativity. A possible route to the solution is through random geometry. Surprisingly, random matrices and random tensors play an important role in this approach. In the first part of the talk, I will present some physical motivations, results and questions concerning these fascinating objects. To that end, I will also remind (or introduce to) some basic concepts of quantum field theory. In the second part of the talk, I will try to describe a remarkable mathematical result discovered recently by Eynard, Orantin and Chekhov, named topological recursion. Coming originally from the so called large N expansion of correlation functions of random matrix models, it shows up in many seemingly unrelated contexts in algebraic geometry, topology, integrable systems... Many of these links are still in conjectural form. I will mainly try to show how to derive the topological recursion for random matrix models.