Wednesday, May 27, 2026
10:00 – 10:45 AM Hao Wu, Tsinghua University
Connection Probabilities for Loop O(n) Models and BPZ Equations
Critical loop O(n) models are conjectured to be conformally invariant in the scaling limit. In this talk, we focus on connection probabilities for loop O(n) models in polygons. Such probabilities can be predicted using two families of solutions to chordal Belavin-Polyakov-Zamolodchikov (BPZ) equations: Coulomb gas integrals and SLE pure partition functions. The conjecture is proved to be true for the critical Ising model, FK-Ising model, percolation, and uniform spanning tree. Recent progress of radial BPZ equations will also be discussed.
10:45 – 11:15 AM Morning Coffee Break
11:15 AM – 12:00 PM Yilin Wang, ETH Zürich
Onsager-Machlup Functional for SLE Loop Measure
Onsager-Machlup functional measures how likely a stochastic process stays close to a given path. SLE is a family of measures on simple paths in the plane introduced by O. Schramm obtained from the Loewner transform of a multiple of Brownian motion. It is well-known that the Onsager-Machlup functional for Brownian motion is the Dirichlet energy. We show that the Onsager-Machlup of the SLE_k loop measure, for any 0 < k \le 4, is expressed using the Loewner energy and the central charge c(k) of SLE_k. Loewner energy is defined as the Dirichlet energy of the Loewner driving function of the loop but it also has tight links to many other fields of mathematics. This is based on the joint work (arXiv: 2311.00209) with Marco Carfagnini (UCSD).
12:00 – 2:00 PM Lunch & Free Afternoon