Erwin Schrödinger Institute, Boltzmanngasse 9, 1090 Vienna, Austria.
The goal of this thematic program is to bring together researchers in mathematics, computer science and theoretical physics in order to make significant progress on the outstanding problems at the interface of combinatorics, geometry and physics. The first point of focus of this program concerns statistical physics on graphs drawn on two-dimensional surfaces. This will be studied in three stages: on a fixed graph, on a random graph, and finally through the study of the interplay between the last two situations as exemplified by the paradigmatic KPZ relation. The list of topics which will be addressed under this heading will include: Tutte polynomials, graph and topological polynomials, the Potts model, relations to knot theory, classical and quantum spin networks, matrix models and two-dimensional quantum gravity, scaling limits of large random maps. The second point of focus concerns attempts at generalizing the two-dimensional success story to the case of higher-dimensional combinatorial random geometries in the light of recent breakthroughs in tensor and group field theories. Here some of the main topics to be addressed are: the 1/N expansion for tensor models, analogues for tensors of the universality for random matrices, renormalizable models of tensor field theory and most likely many other as yet unknown topics which will need to be added to this list due to the fast pace of discovery in this area.
This thematic program will include: