A new bulk Z_2 invariant for interacting phases

The stability of topological indices of condensed matter systems in the p resence of interactions is not expected to hold universally. In this colloquium, I will first discuss the mathematical setup of the classification of interacting phases. I will then focus on a new Z_2 – valued index for time-reversal invariant interacting fermions on infinite lattices and prove its topological stability. I will show that it generalizes the well -known Fu-Kane-Mele index of topological insulators, thereby proving its stability under large perturbations. This is joint work with Alex Bols and Mahsa Rahnama.