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Caltech

Mathematics Colloquium

Wednesday, November 12, 2014
4:00pm to 5:00pm
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Convexity and Subconvexity bounds for automorphic periods and representation theory
Joseph Bernstein, Professor of Mathematics, University of Tel Aviv,

Let Y be a compact Riemann surface with a Riemannian metric of constant curvature -1. Consider the corresponding Laplace-Beltrami operator in the space of functions on Y and fix its eigenfunction $\phi$. Such function is called Maass form; study of such forms plays an important role in Geometry and Number Theory. I will introduce a generalmethod how to bound invariants arising from Maass forms. This method is based on representation theory of the group SL(2, R). I will discuss the following concrete problem. Fix a closed geodesic $C\subset Y$, consider the restriction f of the Maass form $$\phi to C and decompose it into its Fourier series $f=\sum a_n \exp(2\pi int)$. The problem is to give good bounds for Fourier coefficients an when n tends to infinity.

For more information, please contact Pei-Yu Tsai by email at pytsai@caltech.edu or visit http://math.caltech.edu/~numbertheory/.