Paige Hillen (UC Santa Barbara)
Title: Latent symmetry of graphs and stretch factors in Out(Fn)
Abstract: Given an irreducible element of Out(Fn), there is a graph and an irreducible "train track map" on this graph, which induces the outer automorphism on the fundamental group. The stretch factor of an outer automorphism measures the asymptotic growth rate of words in Fn under applications of the automorphism, and appears as the leading eigenvalue of the transition matrix of such an irreducible train track representative. I'll present work showing a lower bound for the stretch factor in terms of the edges in the graph and the number of folds in the fold decomposition of the train track map. Moreover, in certain cases, a notion of the latent symmetry of a graph G gives a lower bound on the number of folds required for any train track map on G. I'll use this to classify all single fold irreducible train track maps.
After the talk, we will gather for tea and snacks in the lounge and then go for dinner with Paige.
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