Title:	Unitary representations of real Lie groups
Speaker:	Peter Trapa
Abstract:	Suppose G is a real reductive Lie group. In its purest form, abstract harmonic analysis asks for a description of the unitary dual of G, the set of equivalence classes of its irreducible unitary representations. For example, if G is the circle group, the unitary dual amounts to the sines and cosines underlying Fourier series. On the other hand, if G is the additive group of real numbers, the unitary dual amounts to the exponential functions appearing in the theory of the Fourier transform. One of the outstanding problems in the subject has been to describe the unitary dual of G in general.