Brownian Bubble Tea - Conformally-Invariant Measures and Brownian Loops

Explore advanced concepts in probability theory and geometry through this 47-minute conference talk that introduces the innovative concept of "Brownian bubble tea" - a Poisson point process on Brownian bubbles rooted on the leaves of a foliation in the punctured disk. Delve into the mathematical framework where Brownian loop measure, a conformally-invariant measure on Brownian loops in the plane originally introduced by Lawler and Werner for studying SLE curves, is disintegrated into Brownian bubble measures along foliation leaves through comparison with the Brownian loop soup. Discover the practical applications of this theoretical breakthrough to several important mathematical objects including Loewner energy of Jordan curves, the Schwarzian action of circle diffeomorphisms, and Loewner-Kufarev energy of foliations. Gain insight into the broader mathematical context surrounding these sophisticated geometric and probabilistic structures, presented as part of IPAM's New Interactions Between Probability and Geometry Workshop, based on collaborative research with Greg Lawler, Fredrik Viklund, and Yilin Wang.