**Title:** Periods of eigenfunctions on symmetric spaces

**Speaker:** Simon Marshall

**Speaker Info:** University of Wisconsin, Madison

**Brief Description:**

**Special Note**:

**Abstract:**

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.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.

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