Advanced talk: 50 years of integral geometry
Prof. Simon Gindikin
Rutgers University, U.S.A.
50 years ago Gelfand suggested a project to reconstruct the harmonic analysis on homogeneous manifolds on the base of some integral transforms of geometric nature similar to Radon's transform. As a result, theory of representations must be a part of much more general geometrical analysis where groups do not participate. I will discuss what is the situation with this project today, 50 years later.