College of Liberal Arts & Sciences

# Operator Theory Seminar

Speaker:

Sayan Das

Topic:

The free group factor problem and Popa's MV-property.

**Abstract:**

One of the most important outstanding problems in von Neumann algebras asks if the group von Neumann algebra of the free group on two generators, denoted by L(F_{2}), is isomorphic to the group von Neumann algebra of the free group on infinitely many generators, denoted by L(F_{∞}). Recently, S. Popa established a roadmap for showing the nonisomorphism of L(F_{2}) and L(F_{∞}). The first step of the proposed roadmap is to establish the so-called mean value property (abbreviated MV-property) for L(F_{2}).

In this talk I shall describe the proof of the result that L(F_{2}) has the MV-property, thereby establishing the first step of Popa's roadmap. This talk is based on a recent joint work with Prof. Jesse Peterson.

Event Date:

October 26, 2021 - 1:30pm to 2:20pm

Location:

VAN 309 or Online (See URL)

Calendar Category:

Seminar

Seminar Category:

Operator Theory