Duncan Dauvergne: Fractal geometry in the KPZ fixed point and the directed landscape

Abstract

The KPZ fixed point and the directed landscape are the two central limiting objects in the KPZ universality class. They arise as scaling limits of classical models in the KPZ universality class, e.g., tasep, Brownian last passage percolation. In this talk, I will explain how to construct these objects from the Airy line ensemble, and how this description leads to surprising Brownian structures and fractal geometry in these objects.