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Explore Kazhdan's Property T and its higher-degree generalizations in this mathematical lecture that examines fundamental analytic invariants of discrete and locally compact groups. Learn how Property T is defined through unitary representations and discover the Delorme-Guichardet characterization using group cohomology vanishing in degree 1 for arbitrary unitary coefficients. Delve into Garland's pioneering higher property T results from the 1970s before examining the Lie group case and their lattices through recent collaborative research. Understand the theoretical foundations that suggest natural extensions to higher-degree Property T and explore practical applications of both classical and higher property T in modern mathematical research.
