The Itzykson Conference is held every year at the Institut de Physique Théorique in Saclay to honour the memory of Claude Itzykson. The 20th edition of this conference, which took place on June 10-12 2015, was devoted to random surfaces and random geometry.
A first theme was the study of random maps, or discretized surfaces, which has recently seen major advances using tools from algebra and geometry (topological recursion, discrete integrability), combinatorics (unified bijections) and probability theory (rigorous construction of the Brownian map, the scaling limit of random maps, and of their local limits).
A second theme was the study of Liouville field theory, a continuous approach to quantum gravity, string theory and random surfaces initiated by Polyakov in 1981, whose mathematical understanding was recently sharpened. Unifying this approach with the discrete one via random maps is a hot topic of research.
A third theme concerned random geometries in higher dimension, in the context of quantum gravity (tensor models, random triangulations, etc) and string theories, which forms another very active area.
Finally, questions concerning random surfaces and random geometries in condensed matter, soft matter, biophysics (interfaces and membranes) and social sciences (complex networks) were also tackled.
Organizing committee: Jérémie Bouttier, François David, Bertrand Eynard and Laure Sauboy (secretary).
Sponsors and benefactors: IPhT (CEA and CNRS), DSM, LabEx LMH, LabEx PALM, ANR Cartaplus, ANR Graal, Fondation Daniel Iagolnitzer, Michael and Victoria Bershadsky