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Quantum Airy structures and topological recursion

Le : 21/02/2018 16h40
Par : Nicolas Orantin (EPFL Lausanne)
Lieu : I 001
Lien web :
Résumé : In the past 10 years, the topological recursion structure discovered in the framework of random matrix theory surprisingly appeared in many other fields of physics and mathematics allowing to solve apparently unrelated problems. Recently, Kontsevich and Soibelman have defined a new representation of this formalism describing the topological recursion as a WKB expansion of a wave function obtained by quantization of a Lagrangian in some symplectic vector space. In this talk, I will review this formalism, called Quantum Airy Structure, its relation with the original recursion as well as its application to the computation of ancestor potentials of cohomological field theories giving access to the corresponding Gromov-Witten invariants. If time allows, I will present how mirror symmetry allows to make explicit computations of such invariants through the definition of a mirror Landau-Ginzburg model.