Algebra Seminar: Michael Bjorklund -- Quasi-morphisms and approximate lattices

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).