Tuesday, September 22, 2020
Math Seminar Series
(Conferences / Seminars / Lectures)
Geometry and Topology more information...
Jeffrey Case from Penn State will be speaking.
The seminar is titled "A geometric approach to fractional powers of the Laplacian and sharp Sobolev trace inequalities."
This meeting will take place online.
The abstract is as follows:
A seminal paper of Caffarelli and Silvestre identifies fractional powers of the Laplacian on Euclidean space as Dirichlet-to-Neumann operators. In this talk, I will use conformal geometry to generalize their approach to Riemannian manifolds. More specifically, I will present multiple (equivalent) definitions of (conformally covariant) operators with principal symbol that of a fractional power of the Laplacian. I will also discuss how these operators lead to a simple derivation of a broad family of sharp Sobolev trace inequalities.