Dietmar Bisch: Subfactors and Quantum Symmetries.
The standard invariant of a subfactor is a complete invariant for amenable, hyperfinite subfactors by a theorem of Popa. It can be viewed as a group-like object and is a certain tensor category of "representations" of the subfactor. However, most hyperfinite subfactors are not amenable, and it is open how to distinguish them. I will discuss constructions of such examples and invariants for them. In particular, I will try to illustrate that a subfactor may encode "quantum symmetries" that are not captured by its standard invariant.
Joan Bosa: The realization problem for von Neumann regular rings.
The realization problem for von Neumann (vN) regular rings asks whether all conical refinement monoids arise from monoids induced by the projective modules over a vN regular ring. We will quickly overview this problem, and show the last developments on it. This is joint work with P.Ara, E. Pardo and A. Sims.