"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.