Geometry and Analysis on Groups Research Seminar

"Geometry and Analysis on Groups" Research Seminar

Time: Dec 12, 2017, 15:15–17:00
Location: Seminarraum 9, Oskar-Morgenstern-Platz 1, 2.Stock
Title: "Fibers of word maps and composition factors."
Speaker: Alexander Bors (Universität Salzburg/Western Australia)
Abstract: To each (reduced) word \(w\), say in \(d\) linearly ordered variables, and each group \(G\), one can associate the so-called word map, \(w_G\colon\thinspace G^d\rightarrow G\), induced by substitution into \(w\). In recent years, there has been an intense interest in these maps, leading to various beautiful and strong results, particularly on images and fibers (i.e., pre-images of one-element sets) of word maps. In our talk, we discuss some recent results, due to Larsen-Shalev and the author, concerning connections between nonabelian composition factors and the size of fibers of nontrivial word maps over (residually) finite groups.