Catherine Wolfram - Brownian bubble tea - IPAM at UCLA
Presenter
January 28, 2026
Abstract
Recorded 28 January 2026. Catherine Wolfram of ETH Zurich presents "Brownian bubble tea" at IPAM's New Interactions Between Probability and Geometry Workshop.
Abstract: Brownian loop measure is a conformally-invariant measure on Brownian loops in the plane introduced by Lawler and Werner to study SLE curves. In this talk, given a foliation of the punctured disk, I will define a Poisson point process on Brownian bubbles rooted on the leaves of the foliation, which we call the Brownian bubble tea along a foliation. By comparing this process to the Brownian loop soup, we show that the Brownian loop measure can be disintegrated into Brownian bubble measures along the leaves of a foliation. I will discuss applications of this result to Loewner energy (of a Jordan curve), the Schwarzian action (of a diffeomorphism of the circle), and Loewner-Kufarev energy (of a foliation), as well as some of the context around these objects. This is based on joint work with Greg Lawler, Fredrik Viklund, and Yilin Wang.
Learn more online at: https://www.ipam.ucla.edu/programs/workshops/new-interactions-between-probability-and-geometry/?tab=overview