Ekaterina Rybak (Vanderbilt University)

Title: Mixed identities and boundary dynamics in weakly hyperbolic groups.

Abstract: A group $G$ is mixed identity free (MIF) if there is no nontrivial word $w ∈ G * F_n$ such that every homomorphism $G * F_n → G$ that is the identity on $G$ sends $w$ to $1$. For groups admitting general-type action on hyperbolic spaces, a pure algebraic condition of being MIF is equivalent to a dynamical condition of an action on the limit set in the Gromov boundary. This gives us a rigidity phenomenon for the group actions. I will discuss this result, its corollaries, and mention the applications to the transitivity degree of weakly hyperbolic groups.

We will gather in the lounge for teatime after the talk, and then we will go for dinner with Ekaterina.