# Overview

The Anti-de-Sitter/Conformal Field Theory (AdS/CFT) correspondence has been dominating research in theoretical high-energy physics for the last 15 years. It posits an exact quantum equivalence between string theory as a theory of quantum gravity on negatively curved space-times and certain conformal quantum field theories defined on the boundary of these space-times. The correspondence is an incarnation of the so-called holographic principle and is viewed as an important clue on the way towards solving the major outstanding mathematical problems of contemporary theoretical physics, quantum gravity and strongly coupled gauge theory. As such, AdS/CFT is bound to find a way into pure mathematics, following the lead of many other, physically substantially simpler, dualities, most notably the correspondence between topological string theory and Chern-Simons gauge theory.

For several years now, methods of integrable systems have taken center stage for the quantitative development of the correspondence. This Thematic Semester, under the aegis of the Mathematical Physics Laboratory of the CRM, will cover a range of topics from the mathematical underpinnings of integrability to a variety of physical applications, up to quantum chromodynamics and condensed matter physics. The focus are those aspects that allow for exact solutions, such as the appearance of integrability in the planar limit of N = 4 super Yang-Mills theory, lower-dimensional models, higher-spin theories, as well as topological field and topological string theories.

This is the first thematic semester in the general area of gauge/gravity duality held at the CRM, and the first time that this ultimate physical duality will be featured at a mathematical research institute anywhere.