PhD, University of Chicago; incoming Ritt Assistant Professor, Columbia University
University of Chicago
Date: April 01, Wednesday, 2026
Time: 14:00-14:50
Host: Minjae Park
Room: Parker 328
Abstract: Liouville quantum gravity (LQG) is a canonical model for a random surface, and in particular a random metric, which in two dimensions enjoys a rich geometric structure including conformal invariance. In higher dimensions, however, the existence of analogous objects remains open. Currently, only subsequential limits of suitable approximations are known to exist, following work of Ding-Gwynne-Zhuang. We show that any such appropriately normalized subsequential limit must satisfy a canonical set of axioms, analogous to those of the two-dimensional LQG metric. In addition, we establish several quantitative properties of these limits, including sharp moment bounds for distances and optimal Holder comparisons with the Euclidean metric. Joint with Zijie Zhuang.