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Explore advanced mathematical concepts in this conference talk examining higher property T and its applications to Banach representations. Delve into Gromov's conjecture regarding L^p-cohomology vanishing for simple groups below the rank, and investigate Farb's conjecture about fixed point properties for lattice actions on CAT(0) cell complexes. Learn how both conjectures follow from a new cohomological vanishing result that represents a Banach version of higher property T. Survey the current state of research in this field and understand the breakthrough contributions that advance our understanding of geometric group theory and representation theory. Discover insights from collaborative research involving cohomological methods and their applications to geometric and algebraic structures in mathematics.
