Recorded 26 January 2026. Franco Vargas Pallete of Arizona State University presents "W-volume for planar domains with circular boundary" at IPAM's New Interactions Between Probability and Geometry Workshop. Abstract: In this talk I'll discuss how to extend the notion of Epstein maps for submanifolds in the conformal boundary of hyperbolic space. That construction will be used to define W-volume for region with circular boundary. I'll discuss then how to use that definition to bound renormalized volume for classical Schottky groups, as well as to give a geometric interpretation for the Loewner energy for sufficiently regular Jordan curves. This is based on join work with Jeff Brock. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/new-interactions-between-probability-and-geometry/?tab=overview