Abstract
I will start the talk with an introduction explaining for non experts the
problems in the theory.The main body of the lecture will consist of two
parts.1)The Selberg trace formula for the exceptional Hecke operators in
connection to the Phillips-Sarnak conjecture on instability of the spectrum of
cusp forms for Hecke congruence groups based on our recent joint work with Erik
Balslev.2)Theorem on the normal distribution of modular symbols,based on the
recent results of Morten Risager and Yiannis Petridis.
Contact person:Uffe Haagerup.