Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Status Confirmed
Seminar Series COURS
Subjects physics
Date Friday 7 October 2022
Time 09:01
Institute IPHT
Seminar Room Salle Claude Itzykson, Bât. 774
Speaker's Last Name Bertrand Eynard
Speaker's First Name
Speaker's Email Address
Speaker's Institution IPhT
Title Introduction to Topological Recursion
Abstract Videoconference: subscribe to the course newsletter to receive links Abstract: \\ Topological Recursion is a mathematical tool. From an initial data S, called the spectral curve, the recursion produces a sequence $\omega_{g,n}(S)$ indexed by two integers g,n. These sequences have many applications that range from string theory to random matrices, statistical physics on a random lattice, integrable systems, WKB asymptotics, CFT, ... We shall introduce Topological Recursion by examples and concrete applications, and mention some long-reach issues. \\ Plan: \\ 1) Introduction by examples of spectral curves: random matrix spectral densities (semi-circle $y=\sqrt{1-x^2}$), the Witten-Kontsevich curve ($y=\sqrt{x}$), and the Mirzakhani's curve ($y=\sin\sqrt{x}$), and their applications, in particular the volumes of the space of hyperbolic surfaces, the Mirzakhani's recursion. \\ 2) Going from examples to general Topological Recursion. Practical methods for computing Topological Recursion, in particular graphical methods, and general properties. \\ 3) Link to the geometry of surfaces: moduli space of Riemann surfaces, cohomological field theories, towards string theory. \\ 4) Topological Recursion as a powerful method to compute WKB series. Link to differential equations and integrable systems.
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