Steven Deprez

My research centers on the study of type II₁ factors. There are many constructions for type II₁ factors, but it is very hard to decide if two, a priori different, constructions give the same type II₁ factor. For example, every ICC group G gives rise to a type II₁ factor LG. But all amenable ICC groups G give the same type II₁ factor LG, which we call the hyperfinite type II₁ factor.

For that reason, various invariants have been introduced, for example the fundamental group (which is not related to the fundamental group of a topological space) and the outer automorphism group. These invariants are usually very hard to compute, but Sorin Popa's deformation/rigidity theory allows us to compute these invariants in specific cases.

Often, type II₁ factors are constructed from groups or from actions of groups on probability spaces. Deformation/rigidity theory uses measurable and geometric properties of these groups and actions. For that reason I am also interested in measurable and geometric group theory.

Currently I am a postdoc at the University of Copenhagen, in the Department of Mathematical Sciences. I am part of the Center for Symmetry and Deformation, and of the research group in Noncommutative Geometry.

I did my PhD with Stefaan Vaes, at the Katholieke Universiteit Leuven, in the section of analysis. My PhD thesis was about computations of invariants of type II₁ factors.