Rylee Alanza Lyman (Rutgers University–Newark)

Title: When is the spine of Outer Space for a free product CAT(0)?

Abstract: Guirardel and Levitt define an Outer Space for a free product of groups inspired by Culler and Vogtmann's Outer Space for the free group. Bridson in his thesis showed that the spine of Culler–Vogtmann Outer Space never supports a "nice" CAT(0) metric when the rank of the free group in question is at least three. CAT(0) geometry, a comparison geometry introduced by Gromov, is a beautiful "fine-scale" geometry providing a common generalization of the geometries of Euclidean and hyperbolic spaces, on the one hand, and certain singular metric spaces, like trees, on the other. In this talk we will completely settle the question of when the spine of Guirardel–Levitt Outer Space admits a "nice" CAT(0) metric. Like Bridson, our results are mostly in the negative, with one surprising family of positive results.

On a separate note, there is a talk on Friday, March 1 at the Quebec Mathematics Colloquium at UdeM by operator algebraist Ilijas Farah which may be of interest to some participants. Wine and cheese will be served after the talk. See here for more info about the talk: https://www.crmath.ca/en/activities/#/type/seminar/id/20342