Seminar

There are some new developments on Plancherel formula and growth of matrix coefficients for unitary representations of nilpotent Lie groups. Those are the groups that look and act like euclidean space with vector addition – and with a built-in uncertainly principle. These developments have consequences for the geometry of weakly symmetric spaces and analysis on "parabolic" subgroups of real semisimple Lie groups, and they have interesting extensions to (infinite dimensional) locally nilpotent Lie groups. I'll describe some standard tools, some new techniques, and several recent results in the area. Background: some group theory, some linear algebra, and some real analysis.