# Jean Pierre Mutanguha (IAS)

Date

Friday November 25, 20222:30 pm - 3:30 pm

Location

Jeffery Hall, Room 234## Math & Stats Department Colloquium

**Friday, November 25th, 2022**

**Time:** 2:30 p.m. **Place:** Jeffery Hall, Room 234

**Speaker:** Jean Pierre Mutanguha (IAS)

**Title:** Finding relative immersions of free groups

**Abstract:** Given an injective endomorphism of a free group, what is the "best" way to represent it so as to read off its dynamical properties? For automorphisms, the prevailing answer since the 1990s has been train tracks and their variations. In this talk, I answer this question for nonsurjective endomorphisms. To some degree, it turns out nonsurjectivity greatly simplifies matters --- a result that I found rather surprising. I proved that all injective endomorphisms can be uniquely represented by certain kinds of expanding immersions on graphs; a bit paradoxically, this representation is trivial when the endomorphism is an automorphism.