Random Maps and Random 2-Dimensional Geometries

Explore the fascinating world of random maps and random 2-dimensional geometries in this Rothschild Lecture delivered by Professor Gregory Miermont from ENS – Lyon. Delve into the concept of maps as graphs embedded into 2-dimensional surfaces, and discover how they can be used to create discrete random metric surfaces. Learn about the expected convergence of large random maps to random metric spaces when distances are appropriately rescaled, drawing parallels to the convergence of random walks to Brownian motion. Examine the irregular nature of these continuum objects and the challenges in applying traditional geometric concepts to them. Investigate the combinatorial tools used to study scaling limits of random maps and consider intriguing conjectures connecting these limits to conformally invariant random fields in the plane. Gain insights into this complex area of mathematics that bridges discrete and continuous geometry, combinatorics, and probability theory.