Title: Quasi-positivity in free groups and braid groups

Date: 04/18/2019

Time: 2:00 PM - 3:00 PM

Place: C304 Wells Hall

I'll discuss joint work with Rita Gitik (UM) on the problem of recognizing quasi-positive elements of a group G defined by
a finite presentation (X ; R). An element of G is quasi-positive if it can be represented by a word that is a product of conjugates of positive powers of letters in X. The recognition problem is to determine whether or not a given word (using both positive and negative powers of letters in X) represents an element of G that is quasi-positive. This problem was solved by Orevkov when G is free with basis X or when G is the 3-strand braid group with its standard generating set. I'll present a new solution to the recognition problem for free groups and discuss some of the challenges posed by braid groups and related groups.