Department of Mathematics  
Seminars  
Address: Mathematics
25337

Caltech

Pasadena,
CA 91125
Telephone: (626) 3954335  Fax: (626) 5851728 
Project MATHEMATICS!  Caltech Home 
Mathematics
Colloquium
2014  2015 
Wednesday, November 12, 2014 4:00 p.m. // 151 Sloan Joseph Bernstein (University of Tel Aviv)  Convexity and Subconvexity bounds for automorphic periods and representation theory Abstract: Let Y be a compact Riemann surface with a Riemannian metric of constant curvature −1. Consider the corresponding LaplaceBeltrami operator in the space of functions on Y and fix its eigenfunction φ. Such function is called Maass form; study of such forms plays an important role in Geometry and Number Theory. I will introduce a general method how to bound invariants arising from Maass forms. This method is based on representation theory of the group SL(2, R). In my talk I will discuss the following concrete problem. Fix a closed geodesic C ⊂ Y, consider the restriction f of the Maass form φ to C and decompose it into its Fourier series f = Σ an exp(2πint). The problem is to give good bounds for Fourier coefficients an when n tends to infinity. Time permitting; I will explain the relation of this problem with the theory of Lfunctions. This is an exposition of my joint works with Andre Reznikov. 
