Type: Seminar

Distribution: World

Expiry: 24 May 2024

CalTitle1: Quasi-morphisms and approximate lattices

Auth: alexs@desktop-h8gjltm.staff.wireless.sydney.edu.au (ashe8718) in SMS-SAML

Michael Bjorklund (Chalmers University) is speaking in the Algebra Seminar this week. We will go out for lunch after the talk. When: Friday 1 March, 12-1pm Where: Carslaw 175 Title: Quasi-morphisms and approximate lattices Abstract: An approximate lattice is a uniformly discrete approximate subgroup Lambda of a locally compact group G for which there is a finite volume Borel set B in G such that B*Lambda = G (* is multiplication). To every such approximate lattice, one can associate a dynamical system of G, which, in the case when Lambda is a lattice coincides with the canonical G-action on the quotient space G/Lambda. In this talk we discuss how one can construct approximate lattices from (cohomologically non-trivial) quasi-morphisms, and show that the corresponding (compact) hulls do not admit any invariant probability measures, and always project to a non-trivial Furstenberg boundary. No prior knowledge of approximate lattices or quasi-morphisms will be assumed. Based on joint work with Tobias Hartnick (Karlsruhe).