## Probabilitic Operator Algebra Seminar: Group measure space von Neumann algebras

Seminar | February 27 | 3-5 p.m. | 736 Evans Hall

Srivatsav Kunnawalkam Elayavalli, UC Berkeley

Department of Mathematics

We begin by talking about probability measure preserving actions of discrete groups, and introduce the notion of the Group Measure Space construction, or the cross product von Neumann algebra. We will then discuss about free and ergodic actions and the measurable functions fixed by these. We will conclude by presenting and proving the key theorem of this talk: The free action on an $L^\infty$ space is ergodic if and only if the corresponding cross product von Neumann algebra is a factor.

dvv@math.berkeley.edu