Activities This Week

This is a joint work with Prof. Ilan Hirshberg and Dr. Tattwamasi Amrutam. Let $\Gamma$ be a discrete group with the property-AP. We give conditions for the inclusion of unital separable C-algebras $A \subset B$ for which every intermediate C-algebra $C$, such that $A \rtimes \Gamma \subset C \subset B \rtimes \Gamma$ is a crossed product. We shall end this talk with some natural classes of inclusion satisfying the above mentioned conditions.

Combinatorial nonpositive curvature of CAT(0) cube complexes plays a surprising role both in topological characterization of hyperbolic 3-manifolds and also in studying algebraic properties of random groups.
With Einstein, Krishna MS, Montee, and Steenbock, we introduce a new model for random quotients of free products that generalizes Gromov’s destiny model. I will discuss challenges that arise in this new setting, connections to work of Futer-Wise and Martin-Steenbock on cubulating quotients, as well as applications to residual finiteness using recent work of Einstein and Groves on relative cubulation.