Description
Back to topA new area of exploration has emerged at the crossroads of probability, geometry, and analysis, aiming to develop a unified theory of the geometry of random structures. The core question is: how does randomness interact with geometry within a given structure? Specifically, does the geometry appear to be random at every scale (i.e. fractal), or do fluctuations “average out” at sufficiently large scales? Can we describe the overall geometry through a suitable scaling limit that permits concrete calculations?
Significant advances have been achieved in this field over the past two decades, yet many fundamental problems remain and the area is developing rapidly. The objective of the workshop is to bring together specialists from probability, mathematical physics, analysis, and related disciplines to examine this issue in key scenarios. The workshop will concentrate on random objects defined either by fundamental probability models or motivated by physics. Key topics of interest include random walks (and many related models), percolation, the Gaussian free field, Schramm-Loewner evolution (SLE), random planar maps, and Liouville quantum gravity, particularly in relation to conformally invariant scaling limits.