SMS scnews item created by Haotian Wu at Wed 4 Mar 2020 0924
Type: Seminar
Distribution: World
Expiry: 3 Jun 2020
Calendar1: 12 Mar 2020 1200-1300
CalLoc1: Carslaw 535A
CalTitle1: Geometry and Topology Seminar: Pengitore -- Unipotent translation-like actions on lattices in semisimple Lie groups
Auth: haotianw@110-174-26-128.static.tpgi.com.au (hawu2800) in SMS-WASM

# Unipotent translation-like actions on lattices in semisimple Lie groups

### Pengitore (Ohio State)

Thursday, 12 Mar 2020, 12:00–13:00, in Carslaw 535.

Seminar schedule

Please join us for lunch after the talk.

Abstract: The Gersten conjecture says that a group being hyperbolic is equivalent to having no Baumslag-Solitar subgroups. This is known to be false due to work of Brady. While there are some weaker versions still open, we are interested in a geometric reformulation of the Gersten conjecture using translation-like actions. To be more specific, the geometric Gersten conjecture asks whether hyperbolicity is equivalent to having no translation-like action by any Baumslag-solitar group. In this talk, we show that cocompact lattices in real semisimple Lie groups admit translation-like actions by cocompact lattices in the unipotent part of the Iwasawa decomposition of the original Lie group. In particular, we demonstrate that $Z_n$ acts translation-like on the fundamental group of any closed hyperbolic $(n+1)$-manifold which provides counterexamples to the geometric Gersten conjecture. This is joint work with Ben McReynolds.

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