17:00
Word maps: properties, applications, open problems
Abstract
Word maps on groups were studied extensively in the past few years, in connection to various conjectures on profinite groups, finite groups, finite simple groups, etc. I will provide background, as well as very recent works (joint with Larsen, Larsen-Tiep,
Liebeck-O'Brien-Tiep) on word maps with relations to representations (e.g. Gowers' method and character ratios), geometry and probability.
Recent applications, e.g. to subgroup growth and representation varieties, will also be described.
I will conclude with a list of problems and conjectures which are still very much open. The talk should be accessible to a wide audience.