Orateur
Uri Bader
(Weizmann Inst. & Univ. of Maryland)
Description
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.
