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Explore the advanced mathematical concept of Higher Property T in this lecture that extends Kazhdan's fundamental Property T beyond its classical formulation. Delve into the analytic invariant of discrete and locally compact groups defined through unitary representations, beginning with the Delorme-Guichardet characterization involving vanishing group cohomology in degree 1 for arbitrary unitary coefficients. Examine Garland's pioneering higher property T result from the 1970s before progressing to contemporary developments in Lie groups and their lattices based on collaborative research with Uri Bader. Discover the applications and implications of both classical and higher property T in modern mathematical research, gaining insight into this sophisticated area of geometric group theory and representation theory.
