Representation theory, Harmonic analysis, Automorphic forms and number theory Ical Atom

Topic of this semester: The Jacquet Langlands correspondence. In the 1970s the Selberg Trace formula was adapted to deal with adele groups and in the hands of Jacquet Langlands became a central tool in the theory of automorphic forms. We shall study a simplified approach to the trace formula that allows to obtain a general version of the correspondence between automorphic forms on GL and automorphic forms on (the units of) division algebras. We shall also study the local aspect of this correspondence. If time permits we shall move to discuss the relative trace formula and its application to the study of periods of automorphic forms, and more recent developments in the direction of GGP conjectures and the Ichino-Ikeda formula.