Title: Multiple Ising interfaces and their relation to Dyson’s circular ensemble.

Abstract:

Conformal invariance of critical lattice models in two-dimensions has been vigorously studied for decades. In this talk, we focus on Ising model on planar domains with mixed plus/minus/free boundary conditions, where multiple interfaces appear naturally. This talk has two parts. In the first part, as a warm-up, we consider critical Ising model on simply connected domains and describe their interfaces using global multiple SLE. In the second part, we explain a relation between multiple Ising interfaces in annulus and Dyson’s circular ensemble. This talk is based on joint works with Eveliina Peltola, Hao Wu and Lu Yang.