University of Sydney Algebra Seminar
Michael Björklund
Friday 1 March, 12-1pm, Place: Carslaw 175
Quasi-morphisms and approximate lattices
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 \(B\Lambda = G\). 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).