Analytic Number Theory and the Trace Formula

I will report on a recent research on the Arthur-Selberg trace formula. The main aim is to get a trace formula explicit enough that it is readily applicable to problems of analytic nature. This research is primarily aimed at studying Langlands’ recent proposal to attack functoriality conjectures, Beyond Endoscopy. In the talk I will briefly describe Beyond Endoscopy and talk about the issues that arise in this context due to singularities of orbital integrals and volumes of tori, and finally describe, for the group GL(2), how one can tackle these problems.