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Explore the extension of Epstein maps for submanifolds in the conformal boundary of hyperbolic space in this 49-minute conference talk. Learn how this construction defines W-volume for regions with circular boundary and discover its applications in bounding renormalized volume for classical Schottky groups. Examine the geometric interpretation of Loewner energy for sufficiently regular Jordan curves through this mathematical framework. Gain insights into the intersection of probability theory and geometry as presented by Franco Vargas Pallete from Arizona State University at IPAM's New Interactions Between Probability and Geometry Workshop, based on collaborative research with Jeff Brock.
