Geometry and analysis of groups and manifolds

Hyperbolic groups and minimal varieties in Hilbert spherical quotients

speaker: Antoine Song (University of California)

abstract: Given a closed oriented manifold M, the spherical volume of M is a topological invariant introduced by Besson-Courtois-Gallot in their work on the entropy rigidity problem. The spherical volume naturally corresponds to a volume minimization problem inside a quotient of the Hilbert sphere. The main result we will discuss is that if M is negatively curved, then its spherical volume is equal to the volume of a minimal variety inside a quotient of the Hilbert sphere. Some important tools involved in the construction are the theory of metric currents, and properties of the regular representation of hyperbolic groups.

timetable:
Thu 29 Jun, 14:00 - 15:00, Aula Dini
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