Speaker: Eveliina Peltola
Affiliation: Aalto University, Finland and University of Bonn, Germany
Title of Talk: On geometric properties of conformally invariant curves
Date: January 07, 2026
Time: 11:30:00 Hours
Venue: A-369

Abstract: How to construct a canonical random conformally invariant path in two dimensions? Motivated by Loewner's classical theory of dynamics of slit domains, Schramm introduced random Loewner evolutions to model canonical random curves via evolutions of conformal maps. While the initial usage of such Schramm-Loewner evolutions (SLEs) was to describe critical interfaces in statistical physics models and their relation to conformal field theory (CFT), SLE type curves quickly turned out to be ubiquitous in various problems in probability theory and mathematical physics, and to have intricate connections to complex geometry and beyond. This talk highlights some geometric aspects emerging from the study of SLE curves and CFT. As examples, we shall mention versions of the Loewner energy (the anticipated action functional of these canonical curve models, or more rigorously, the rate function in large deviations principles for the random curves), classification problems of covering maps with prescribed critical points, and if time permits, the emergence of the Virasoro algebra (the symmetry algebra of CFTs) from complex deformations of boundaries of bordered Riemann surfaces (i.e., loops).