Research

My main research area is Operator Algebras and their interactions with Dynamical Systems, Geometric Group Theory and Representation Theory with the following topics:

• Property A and coarse embedding in coarse geometry;

• Approximation properties for simple Lie groups and groupoid dynamical systems;

• The Baum-Connes conjecture for algebraic groups;

• Rigidity, Structure and K-theory of lp uniform Roe algebras;

• Structure and Dimension theories for étale groupoid C*-algebras;

• Counterexamples to the coarse Baum–Connes conjecture;

• Measured (asymptotic) expanders;

• Regularity properties for ample groupoids and general C*-algebras in classification;

• Commensurated subgroups (a.k.a. Hecke pairs) in coarse geometry and operator algebras.