Abstracts

Camille Horbez - Abstract commensurators of some normal subgroups of Out(Fn)

Abstract : We give a new proof of a theorem of Farb and Handel stating that for all n\ge 4, Out(Fn) is equal to its own abstract commensurator. In other words, every isomorphism between finite-index subgroups of Out(Fn) is the restriction of the conjugation by some element of Out(Fn). Our proof enables us to extend their theorem to the n=3 case. More generally, we prove that many normal subgroups of Out(Fn), for example the Torelli subgroup IA_n and all subgroups in the Johnson filtration of Out(Fn), have Out(Fn) as their abstract commensurator. This is a joint work with Martin Bridson and Ric Wade.

Christopher Leininger - Polygonal billiards, Liouville currents, and rigidity
Abstract: A particle bouncing around inside a Euclidean polygon gives rise to a biinfinite "bounce sequence" (or "cutting sequence") recording the (labeled) sides encountered by the particle. In this talk, I will describe recent work with Duchin, Erlandsson, and Sadanand, in which we prove that the set of all bounce sequences---the "bounce spectrum"---essentially determines the shape of the polygon. This is consequence of our main result about Liouville currents on surfaces associated to nonpositively curved Euclidean cone metrics. In the talk I will explain the objects mentioned above, how they relate to each other, and give some idea of the proof of the main theorem.

Karen Vogtmann - Feynman amplitudes and Outer space
Abstract: Recent work of Bloch and Kreimer has indicated that certain rules used by physicists for computing Feynman amplitudes in quantum field theories are related to the structure of Outer space, in particular to the combinatorics of both the spine and the Bestvina-Feighn bordification. I will attempt to explain this relationship.