Intersections of Topological Recursion, Conformal Field Theory, and Random Geometry

A two-dimensional conformal field theory (2D-CFT) is a quantum field theory on a Euclidean two-dimensional space, that is invariant under local conformal transformations. In contrast to other types of conformal field theories, 2D-CFTs have infinite-dimensional symmetry algebras. In some cases, this allows them to be solved exactly — at least in the physics sense. Mathematicians have made some recent breakthroughs towards understanding of 2D-CFT, and this workshop aims to bring together researchers with very different viewpoints and expertise on this multifaceted topic.
We plan to focus on the interrelations of 2D-CFT with two other topical research areas in mathematics: Random Geometry and Topological Recursion. The former is a general research area of random curves and surfaces, pertaining to understanding critical interfaces in statistical physics models (SLE and CLE) on the one hand and models for quantum gravity (Liouville theory) on the other hand. The latter is a universal recursive relationship between various invariants: a computational scheme related to the combinatorics of pair of pants on surfaces, for solutions of certain systems of compatible linear, often infinite-dimensional, partial differential equations. The main vision of the organizers is that these three topics have several links to each other, which however are not yet known in detail, and thus the main goal of this workshop will be to focus on the triangle of relations between them.