Uri Bader - Higher property T, Banach Representations and Applications

Gromov conjectured that the L^p-cohomology of simple groups vanishes below the rank. Farb conjectured a fixed point property for actions of lattices in such groups on CAT(0) cell complexes of dimension lower than the rank. Both conjectures follow from a new cohomological vanishing result, which could be seen as a Banach version of higher property T. In my talk I will survey the subject and explain the new contribution. Based on a joint work with Saar Bader, Shaked Bader and Roman Sauer. Uri Bader (Weizmann Institute) === Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community. ===