Brent Nelson, Michigan State University
Closable derivations are anticoarse, of course
The anticoarse space of an inclusion $N\subset M$ of tracial von Neumann algebras is an $N$-subbimodule of $L^2(M)$ whose size is sensitive to several structural properties of the inclusion. It has become a staple of so-called microstates techniques in free probability, where it allows one to parlay finite dimensional approximations into algebraic properties. On the other hand, non-microstates techniques, which exploit the regularity of certain derivations on a von Neumann algebra, have not made use of the anticoarse space, until now. In this talk, I will discuss how deformations given by closable derivations provide a natural connection to anticoarse spaces and consequently yield new applications of free probability. This is based on joint work with Yoonkyeong Lee.
QNC 1507 or Join on Zoom