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Thursday, January 17, 2019

**Abstract:** For automorphisms of the free group $F_r$, being "fully irreducible" is the main analog of the property of being a pseudo-Anosov element of the mapping class group. It has been known, because of general results about random walks on groups acting on Gromov-hyperbolic spaces, that a "random" (in the sense of being generated by a long random walk) element $\phi$ of $Out(F_r)$ is fully irreducible and atoroidal. But finer structural properties of such random fully irreducibles $\phi\in Out(F_r)$ have not been understood. We prove that for a "random" $\phi\in Out(F_r)$ (where $r\ge 3$), the attracting and repelling $\mathbb R$-trees of $\phi$ are trivalent, that is all of their branch points have valency three, and that these trees are non-geometric (and thus have index $<2r-2$). The talk is based on a joint paper with Joseph Maher, Samuel Taylor and Catherine Pfaff.

Thursday, January 24, 2019

Tuesday, January 29, 2019

Tuesday, February 5, 2019

Tuesday, February 26, 2019

Thursday, March 14, 2019

Thursday, March 28, 2019

Thursday, April 18, 2019

Thursday, April 25, 2019