3:00–4:00 pm Eckhart 206
Title: Permutations and Random Geometry
Abstract:
In recent years, surprising connections have emerged between the theory of random permutations and random geometric objects arising in probability, statistical mechanics, and quantum physics. On one side are permutons, which describe scaling limits of large permutations; on the other are random planar maps, Schramm–Loewner evolution curves, and Liouville quantum gravity surfaces.
In this talk, I will discuss some of these new links, with a particular emphasis on analogies between two classical problems: the longest increasing subsequence in a random permutation and the longest directed path in a random planar map. I will describe recent progress on this circle of ideas and explain how it points toward a new notion of directed Liouville quantum gravity metric.