**INFINITE GROUPS SEMINAR 2011****Location:**Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle**Time and Date:**12:00 pm, Mon, 14^{th}Feb 2011**Speaker:**Adam Piggott, Department of Mathematics, Bucknell University**Title:***The automorphisms of McCullough-Miller space***Speaker:**Prof George Willis, CARMA, The University of Newcastle**Title:***Rigidity of Homomorphisms from Arithmetic Groups to Totally Disconnected Groups***[Permanent link]**
McCullough-Miller space X = X(W) is a topological model for the outer automorphism group of a free product of groups W. We will discuss the question of just how good a model it is. In particular, we consider circumstances under which Aut(X) is precisely Out(W). The talk will explain joint work with Yehuda Shalom showing that the only homomorphisms from certain arithmetic groups to totally disconnected, locally compact groups are the obvious, or naturally occurring, ones. For these groups, this extends the supperrigidity theorem that G. Margulis proved for homomorphisms from high rank arithmetic groups to Lie groups. The theorems will be illustrated by referring to the groups $SL_3(\mathbb{Z})$, $SL_2(\mathbb{Z}[\sqrt{2}])$ and $SL_3(\mathbb{Q})$. |