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Submitted by sde on 29 December, 2014 - 14:25

Date/Time:

Monday, January 12, 2015 - 11:35 to 12:35

Venue:

LH 101

Speaker:

Dr. Pritam Ghosh

Title:

Dynamics of outer automorphisms of free groups

Abstract: We will first look at some geometric properties of a free group and follow it up by introducing the Train track theory which is a vital tool for studying dynamics of outer automorphisms of free groups. Given a finite rank free group $F$ of rank $\geq 3$ and two exponentially growing outer automorphisms $\psi$ and $\phi$ with dual lamination pairs $\Lambda^\pm_\psi$ and $\Lambda^\pm_\phi$ associated to them, which satisfy a notion of independence described in this paper, we will use the pingpong techniques developed by Handel and Mosher to show that there exists an integer $M > 0$, such that for every $m,n\geq M$, the group $G_M=\langle \psi^m,\phi^n \rangle $ will be a free group of rank two and every element of this free group which is not conjugate to a power of the generators will be fully irreducible and hyperbolic.

**School of Mathematical Sciences**

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