Geometry, Topology and Dynamics Seminar
Aleksander Skenderi
University of Wisconsin-Madison
Free semigroups of large critical exponent
Abstract: For a broad class of convergence groups, we construct free subsemigroups having critical exponents arbitrarily close to, but strictly less than, the critical exponent of the ambient convergence group. I'll explain how to apply this result to a particular class of discrete subgroups of Lie groups known as transverse groups, and also explain how our result implies a counterpart to a classical gap theorem of Kevin Corlette concerning discrete subgroups of the isometry groups of quaternionic hyperbolic space and the Cayley (octonionic) hyperbolic plane.
I will also briefly mention work in progress (to appear hopefully by the end of the month on the arXiv) which shows analogous results for any Zariski dense discrete subgroup of a semisimple real Lie group G.
I'll introduce these notions from scratch and try to focus on their relations to (hopefully more familiar) concepts in real hyperbolic geometry. Time permitting, I'll discuss the general framework in which we prove these results.
Wednesday September 3, 2025 at 3:00 PM in 636 SEO