The Conformal Dimension and Minimality of Stochastic Objects
Time: 2023-03-20
Published By: He Liu
Speaker(s): Wenbo Li(Peking University)
Time: 14:00-15:00 March 27, 2023
Venue: Room 1114, Sciences Building No. 1
The conformal dimension of a metric space is the infimum of the Hausdorff dimension among all its quasisymmetric images. We develop tools related to the Fuglede modulus to study the conformal dimension of stochastic spaces. We first apply our techniques to construct minimal (in terms of conformal dimension) planar random graph. We further develop this line of inquiry by proving that a "natural" stochastic object, the graph of the one dimensional Brownian motion, is almost surely minimal. If time permits, we will discuss further developments on Lévy processes.
Bio: Wenbo Li is currently a Postdoc Scholar at Beijing International Center for Mathematical Research, Peking University. He obtained his Ph.D. in Mathematics in 2022 at the University of Toronto under the supervision of Professor Ilia Binder. His research is focused on random geometry, analysis on metric measure spaces, and metric geometry. His current interest is to apply the techniques in metric geometry to problems in the random world.
