Colloquium: L^p norms and global harmonic analysis.

Event Type: 
Matthew Blair
Event Date: 
Thursday, September 14, 2017 -
3:30pm to 4:30pm
SMLC 356

Event Description: 

Title: L^p norms and global harmonic analysis.


We consider eigenfunctions of the Laplacian on a compact Riemannian manifold, which generalize classical vibrational modes on strings and plates.  In particular, we are interested in estimating their L^p norms in the high frequency limit as a means of measuring the strength of their amplitudes and understanding their concentration profiles.

In the 1980's, Sogge showed that there are a family of upper bounds on L^p norms of eigenfunctions which are "universal" in that they are satisfied on any compact manifold.  However, they typically do not deliver the optimal bound.  In this talk, we will discuss L^p norms and mass concentration properties of eigenfunctions and how they relate to the global dynamics of the geodesic flow underlying the manifold.  We then consider the particular case of manifolds with nonpositive sectional curvatures with an eye on recent improvements in the known L^p bounds on eigenfunctions in this setting.

Event Contact

Contact Name: Matthew Blair