Generalized Willmore Energies and Renormalized Volumes
Speaker: Andrew Waldron, UC Davis
Abstract: Conformally embedded hypersurfaces have a rich invariant theory—both local and integrated. Invariants of a hypersurface embedded in a conformal manifold include higher dimensional analogs of the celebrated Willmore energy. These can be studied by viewing the hypersurface as a conformal infinity for a Riemannian manifold whose metric obeys a singular analog of the Yamabe problem. Non-trivial invariants are then obtained through the volume asymptotics of regions approaching the singularity, and for hypersurfaces with boundary also by areas of a related singular minimal surface problem. These methods were inspired in part by physics applications to the Anti de Sitter—Conformal Field Theory correspondence.
Room Reservation Information
Room Number: 106 McAllister
Time: 2:30pm - 3:30pm