# Program

This program is devoted to the investigation of universal analytic and geometric objects that arise from natural probabilistic constructions, often motivated by models in mathematical physics. Prominent examples for recent developments are the Schramm-Loewner evolution, the continuum random tree, Bernoulli percolation on the integers, random surfaces produced by Liouville Quantum Gravity, and Jordan curves and dendrites obtained from random conformal weldings and laminations. The lack of regularity of these random structures often results in a failure of classical methods of analysis. One goal of this program is to enrich the analytic toolbox to better handle these rough structures.

**Keywords and Mathematics Subject Classification (MSC)**

**Tags/Keywords**

geometric universality

random metric spaces

growth processes

SLE

conformal welding

random surfaces

uniformization

**Primary Mathematics Subject Classification**

37Fxx - Dynamical systems over complex numbers [See also 30D05, 32H50]

37F34 - Teichmüller theory; moduli spaces of holomorphic dynamical systems [See also 37F31, 37F32]

**Secondary Mathematics Subject Classification**

30C85 - Capacity and harmonic measure in the complex plane [See also 31A15]

30F45 - Conformal metrics (hyperbolic, Poincaré, distance functions)

30F60 - Teichmüller theory for Riemann surfaces [See also 32G15]

60Bxx - Probability theory on algebraic and topological structures

60J80 - Branching processes (Galton-Watson, birth-and-death, etc.)

January 19, 2022 - January 21, 2022 | [HYBRID WORKSHOP] Connections Workshop: The Analysis and Geometry of Random Spaces |

January 24, 2022 - January 28, 2022 | [HYBRID WORKSHOP] Introductory Workshop: The Analysis and Geometry of Random Spaces |

March 28, 2022 - April 01, 2022 | The Analysis and Geometry of Random Spaces |