##### Department of Mathematics,

University of California San Diego

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### Math 209: Number Theory Seminar

## Simon Marshall

#### Wisconsin

## Large values of eigenfunctions on hyperbolic manifolds

##### Abstract:

It is a folklore conjecture that the sup norm of a Laplace eigenfunction on a compact hyperbolic surface grows more slowly than any positive power of the eigenvalue. In dimensions three and higher, this was shown to be false by Iwaniec-Sarnak and Donnelly. I will present joint work with Farrell Brumley that strengthens these results, and extends them to locally symmetric spaces associated to $\mathrm{SO}(p,q)$.

[pre-talk at 1:20PM]

### February 9, 2023

### 2:00 PM

APM 6402 and Zoom; see https://www.math.ucsd.edu/~nts

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