Special Day on Eigenfunctions of the Laplacian on manifolds

Title: Focal points and sup-norms of eigenfunctions
Speaker: Chris Sogge
Speaker Info: Johns Hopkins
Brief Description:
Special Note:

If (M,g) is a compact real analytic Riemannian manifold, we give a necessary and sufficient condition for there to be a sequence of quasimodes saturating sup-norm estimates. The condition is that there exists a self-focal point in M for the geodesic flow at which the associated Perron-Frobenius operator has a nontrivial invariant function. The proof is based on von Neumann's ergodic theorem and stationary phase. In two dimensions, the condition simplifies and is equivalent to the condition that there be a point through which the geodesic flow is periodic. This is joint work with Steve Zelditch.
Date: Saturday, October 25, 2014
Time: 11:30am
Where: Harris L28
Contact Person: Valentino Tosatti
Contact email: tosatti@math.northwestern.edu
Contact Phone:
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