Title: The generalized doublingmethod and its applications
Abstract: The doubling method,first introduced by Piatetski-Shapiro and Rallis in the 80s, has had numerousapplications, e.g. to the theta correspondence and to arithmetic problems.In a series of recent works this method was generalized in severalaspects, with an application to functoriality from classical groups to GL(N).The most recent result is a multiplicityone theorem (joint work with Gourevitch and Aizenbud).
I will brieflysurvey the method and talk about some of its applications.
Parts of the talk arealso based on a collaboration with Cai, Friedberg and Ginzburg.