Oberseminar Topologie: 23.06.2025 Claudio Llosa Isenrich (Karlsruhe Institute of Technology) Title: $L^p$ measure equivalence classification of nilpotent groups Abstract: A famous open problem in geometric group theory is the quasi-isometry classification of nilpotent groups. Conjecturally, two simply connected nilpotent Lie groups are quasi-isometric if and only if they are isomorphic. In the 1980s, Pansu reduced this conjecture to nilpotent groups with isomorphic associated Carnot graded group. I will explain how measured group theory can offer a route towards making progress on this conjecture. In particular, I will present a converse to a theorem of Austin, proving that two finitely generated or simply connected nilpotent groups have isomorphic associated Carnot graded groups if and only if they are integrably measure equivalent. More generally, I will classify simply connected nilpotent Lie groups up to $L^p$ measure equivalence for every $p\leq 1$. This is joint work with Thiebout Delabie and Romain Tessera.