This volume is based on four advanced courses held at the Centre de Recerca Matemàtica (CRM), Barcelona. It presents both background information and recent developments on selected topics that are experiencing extraordinary growth within the broad research area of geometry and quantization of moduli spaces. The lectures focus on the geometry of moduli spaces which are mostly associated to compact Riemann surfaces, and are presented from both classical and quantum perspectives.

Autorentext

Vladimir V. Fock is Professor at the Institut de Recherche Mathématique Avancée in Strasbourg. Andrey Marshakov is Professor at the National Research University Higher School of Economics in Moscow.Florent Schaffhauser is Associate Professor at Universidad de Los Andes in Bogotá.

Constantin Teleman is Professor at the University of California in Berkeley.

Richard A. Wentworth is Professor at the University of Maryland.

Inhalt

Loop groups, clusters, dimers and integrable systems.- Lectures on Klein surfaces and their fundamental group.- Five lectures on topological field theory.- Higgs bundles and local systems on Riemann surfaces.