Type: Seminar

Distribution: World

Expiry: 26 Sep 2013

Auth: zhangou@como.maths.usyd.edu.au

Speaker: Dr. Simon Marshall (Northwestern) http://www.math.northwestern.edu/~slm/ Time: Thursday, August 29, 12NOON--1PM Room: Carslaw 707A Lunch: after the talk, at Law Annex Cafe. ---------------------------------------------- Title: L^p Bounds for Eigenfunctions on Locally Symmetric Spaces Abstract: there is a classical theorem of Sogge which provides bounds for the L^p norms of a Laplace eigenfunction on a compact Riemannian manifold, which are sharp on the sphere and for spectral clusters. I will present a generalization of this theorem to eigenfunctions of the full ring of invariant differential operators on a locally symmetric space, as well as a theorem on the restriction of eigenfunctions to maximal flat subspaces. Time permitting, I will discuss ways in which these bounds can be improved using inputs from number theory. ---------------------------------------------- Seminar website: http://www.maths.usyd.edu.au/u/SemConf/Geometry/