2017 : Résurgence et quantification


Le 7ème Séminaire Itzykson, portant sur le thème "Résurgence et quantification" se tiendra à l'IHÉS le jeudi 20 avril 2017.


Marcos Mariño (Genève): Quantum theory and non-perturbative effects

Abstract: Divergent series are ubiquitous in quantum theory, and one should learn to live with them and eventually make sense of them. A general framework to address these issues is the theory of resurgence by Ecalle. This requires the introduction of trans-series, or generalized formal series incorporating exponentially small effects, which are invisible in classical asymptotics. I will present the general framework of resurgence in down-to-earth terms, and discuss various examples in the theory of differential equations, Quantum Mechanics and in some (simple) Quantum Field Theories. In the last part of the talk I will summarize recent progress in the application of this program to topological string theory.

Sergei Gukov (Caltech):  Resurgence and Modularity

Abstract: Why do modular forms tend to have integer coefficients in their q-expansion? Are they counting something? And, can we "categorify" a modular form by representing it as a graded Euler characteristic of some homology theory? There are several ways to answer these questions, e.g. the one based on classical theory of modular forms relates them to counting points on elliptic curves and motives of higher-dimensional varieties. In this talk, we will ask these questions for mock modular forms, introduced by Ramanujan. They also exhibit q-expansion with integer coefficients and, surprisingly, the answer to these question is based on resurgent analysis of a different power series, which at first shows no signs of integrality!

Maxim Kontsevitch (IHES):  Semi-infinite topology of the complexified path integral.

Abstract: I will explain a viewpoint on resurgence via Floer-type topology of Lefschetz thimbles in the complexified path integral. In particular, so called 2d-4d wall-crossing formalism of Gaiotto, Moore and Neitzke arises naturally in this framework, without any reference to supersymmetric field theories.

Ricardo Schiappa (Lisbonne & CERN): Resurgence Asymptotics in String Theory

Following up on the morning lecture, I will give a very light introduction to resurgent asymptotics. These techniques will then be explored (again in the spirit of a light introduction) within transseries solutions of topological string theory, themselves obtained via a nonperturbative completion of the holomorphic anomaly equations.