The 21st Takagi Lectures
June 23 (Sat), 2018
10:05--11:05, 14:00--15:00
Lecture Hall (Room No. 420)
Research Institute for Mathematical Sciences
Kyoto University, Kyoto, Japan

Brownian Geometry
Jean-François Le Gall
(Université Paris-Sud)


We present different continuous models of random geometry that have been introduced and studied in the recent years. In particular, we consider the Brownian map, which is the universal scaling limit of large planar maps in the Gromov--Hausdorff sense, and the Brownian disk, which appears as the scaling limit of planar maps with a boundary. We discuss the connections between these models, and we emphasize the role played by Brownian motion indexed by the Brownian tree.