Monday October 6th, 12:30, CRM Small room
Speaker: Sean Cleary, The City College of New York
Title: Rotation distances and generating sets for Thompson's group F
Abstract: Rotation distances measure differences in tree shape between binary trees, by counting a minimum number of rotations needed to transform a first given tree into another. These correspond to word metrics for Thompson's group F with respect to different generating sets, depending upon where rotations are allowed. These connections give useful results in both directions.
Second talk, 13:30
Speaker: Laura Ciobanu, Université de Fribourg
Title: Properties of generic subgroups of free and hyperbolic groups
Abstract: Let F be a finitely generated free group, and K be a finitely generated, infinite index subgroup of F. We show that generically many finitely generated subgroups H have trivial intersection with all conjugates of K, thus proving a stronger, generic form of the Hanna Neumann Conjecture. As an application, we show that the equalizer of two free group homomorphisms is generically trivial, which implies that the Post Correspondence Problem is generically solvable in free groups. Then let G be a word hyperbolic group. We show that generically, finitely generated subgroups of G are free and quasiconvex. This is joint work with Armando Martino and Enric Ventura.
