Higher Property T - Cohomological Vanishing and Fixed Point Properties

Explore advanced mathematical concepts in this 57-minute conference talk that connects three distinct mathematical phenomena through a unified cohomological framework. Examine Gromov's conjecture regarding the vanishing of Lp-cohomology of simple groups below the rank, alongside Farb's conjecture about fixed point properties for lattice actions on CAT(0) cell complexes. Discover how recent work by Loewe-Frazcyk and Bader-Sauer suggests waist inequalities for locally symmetric spaces up to the rank. Learn about a new cohomological vanishing result that serves as a Banach version of higher property T, which provides proofs for both Gromov's and Farb's conjectures while offering additional evidence for the waist inequality conjecture. Delve into this joint research with Uri Bader, Saar Bader, and Shaked Bader, presented during the thematic meeting on "Orbit equivalence and topological and measurable dynamics" at the Centre International de Rencontres Mathématiques in Marseille, France.