Analysis and Geometry of Random Shapes

January 7 - 11, 2019


AGR_ImageIn recent years the investigation of analytic and geometric objects that arise from natural probabilistic constructions has gained a lot of attention. Often these probabilistic constructions are motivated by models in mathematical physics. Prominent examples for some recent developments are the stochastic Loewner equation (SLE), the continuum random tree (CRT), the Brownian sphere, Bernoulli percolation on the integers, random surfaces produced by Liouville Quantum Gravity” (LQG), or curves obtained from random conformal weldings. There is some indication that concepts from quasiconformal analysis and geometry are relevant for the exploration of these topics, but it is likely that one has to extend the scope of the classical theory.

The aim of the workshop is provide an opportunity for a fruitful interaction between complex analysts, geometers, and probabilists. The underlying general philosophy is the desire to extend deterministic methods from conformal geometry and analysis for potential applications in probabilistic settings that arise in modern research. We want to bring together mathematicians with diverse research backgrounds to identify interesting problems for the study of random shapes generated by relevant probabilistic models and foster the development of the necessary analytic tools for their investigation.

Organizing Committee

Mario Bonk (University of California, Los Angeles (UCLA), Mathematics)
Joan Lind (University of Tennessee)
Steffen Rohde (University of Washington)
Eero Saksman (University of Helsinki)
Fredrik Viklund (Royal Institute of Technology (KTH))
Jang-Mei Wu (University of Illinois at Urbana-Champaign)