Title: Periods of eigenfunctions on symmetric spaces
Speaker: Simon Marshall
Speaker Info: University of Wisconsin, Madison
Let X be a compact locally symmetric space, and Y a locally symmetric subspace. Let f be an eigenfunction of the invariant differential operators on X with eigenvalue tending to infinity. I will discuss the problem of bounding the period and Fourier coefficients of f along Y, and the L^2 norm of f restricted to Y, for a range of different X and Y. I will present results on this problem that use a combination of techniques from harmonic analysis and the theory of automorphic forms, although no knowledge of automorphic forms will be assumed in the talk.Date: Monday, February 05, 2024
In particular, I will present a result in the case when X and Y are hyperbolic manifolds, which bounds the Fourier coefficients < f, f' > when f and f' are Laplace eigenfunctions on X and Y whose frequences have bounded difference. In the hyperbolic case, this strengthens a theorem of Zelditch on Fourier coefficients of eigenfunctions on general Riemannian manifolds.