WoG 2024 Talk 4.5: Antonio López Neumann - On $L^p$-cohomology of semisimple groups

Speaker: Antonio López Neumann
Institution: IMPAN (Warsaw)
Website: sites.google.c...
Title: On $L^p$-cohomology of semisimple groups
Abstract: $L^p$-cohomology ($1\lt p\lt \infty$) is a quasi-isometry invariant popularized by Gromov. He conjectured that for semisimple groups, $L^p$-cohomology vanishes in degrees below the rank for all $1\lt p\lt \infty$ and that it is sometimes nonzero in degree equal to the rank. These conjectures are known to be true when the degree is 1, but for higher degrees only partial results have been obtained. This talk will present general aspects of $L^p$-cohomology, as well as some new results around these questions, such as vanishing in degree 2 and non-vanishing in degree equal to the rank.