Resurgencia es un método utilizado para resolver equaciones dife-renciales, con un amplio rango de aplicaciones. Se basa principalmen-te en la aplicación del llamado Alien Calculus. Tiene su origen en elanálisis del fenómeno de Stokes, que en análisis complejo consiste enque el comportamiento asintótico de ciertas funciones puede variar endistintas regiones del plano complejo. Resurgencia nos dirá cómo rela-cionar estos dos comportamientos, es decir, cómo cruzar las llamadaslíneas de Stokes, las cuales separan dichas regiones.La principal característica de Resurgencia es que es un procesoconstructivo que nos permite extraer información sobre soluciones for-males dadas en forma de transseries (series de potencias, logaritmos yexponenciales) con radio de convergencia nulo.En esta charla daremos una pequeña noción sobre dónde aplicamosResurgencia e introduciremos los conceptos y procedimientos acom-pañados de un ejemplo ilustrativo.

The goal of this seminar is to introduce the concept of integrability, showing how it can be applied to obtain solutions for dynamical systems. We will then apply the tools that we build in the first part of the talk to attack a problem that is relevant in topological string theory, the problems of the KP and KdV hierarchy. We will introduce those problems in a self-contained way, explore the use of the technique of the Lax pairs to solve them and finally we will see how those solutions are of use in matrix models, that appear in minimal string theories of interest.

We start by a review of numerical and analytical conformal bootstrap techniques at our disposal. We then use these tool to approach the “simplest” Argyres-Douglas theory, a four-dimensional N=2 strongly coupled superconformal field theory. We “zoom in” to the theory by specifying Coulomb branch data, and obtain strong constraints on its operator spectrum and OPE coefficients. We conclude with an outlook for the prospects of approaching other strongly coupled N=2 conformal theories.

Mirror Symmetry is a conjecture that suggests the connection between the structures of two mirror manifolds. In this talk, we will present an introduction to this symmetry, first through the Strominger-Yau-Zaslow conjecture and then in more general terms. Finally, we will mention the origin of Mirror Symmetry in the context of Topological Strings and we will make some comments on the topological A and B models.

The non-equilibrium hydrodynamic phenomena in strongly coupled quantum systems such as the N=4 supersymmetric Yang-Mills plasma, can be addressed with the tools of the AdS/CFT correspondence, where calculations in the gravity side of the duality can be performed through a large proper-time expansion. This expansion is asymptotic and encodes a spectrum of non-hydrodynamic modes reflecting the frequencies of AdS black-brane quasinormal modes. The emerging structure for the description of physical quantities such as the energy density is of a resurgent transseries. The theory of resurgence perfectly captures this perturbative/non-perturbative connection and its consequences. Moreover, it allows us to construct a full non-perturbative solution from perturbative data. In this talk, I will analyse essential role of resurgence theory, coupled to exponentially accurate numerical methods, to go beyond the perturbative results and obtain non-perturbative data. I will use these techniques to thoroughly study the resurgent transseries for the energy density of the N=4 SYM plasma.

We start by a review of numerical and analytical bootstrap techniques at our disposal. We then use these tool to approach the “simplest” Argyres-Douglas theory. Specifically, we attempt to “zoom in” to the theory by specifying Coulomb branch data, and obtain constraints on its operator spectrum and OPE coefficients. We conclude with an outlook for the prospects of approaching other Argyres-Douglas theories.

Resurgence is a method used to solve differential equations with a wide range of applications. It is based on the so called alien calculus. The talk will give a brief insight on what resurgence is used for. Then, via example, a short introduction to alien calculus is given.

This is the third in a series of talks introducing the subject of resurgence in quantum mechanics, field theory and string theory.

This is the second in a series of talks introducing the subject of resurgence in quantum mechanics, field theory and string theory.

This is the first in a series of talks introducing the subject of resurgence in quantum mechanics, field theory and string theory.

We will describe a method for constructing geodesics on the space of Kähler metrics on a compact Kähler manifold. Applications to geometric quantization will also be discussed.