##### Department of Mathematics,

University of California San Diego

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### Advancement to Candidacy

## Daniel Hoff

#### UCSD

## Von Neumann Algebras of Equivalence Relations with Nontrivial One-Cohomology

##### Abstract:

A prevailing question in the study of von Neumann algebras asks to what extent certain algebras constructed from groups and their actions "remember" the original group and action. Pursuing this question led naturally to the study of von Neumann algebras coming from certain equivalence relations as well. Though a large class of groups and actions which produce "forgetful" algebras have been known since the 1970s (due to Connes and Zimmer), very little progress was made outside of this class until a breakthrough by Sorin Popa some 30 years later. We will give an overview of Popa's powerful deformation/rigidity theory, state a recent result for von Neumann algebras of equivalence relations, and discuss future directions of research.

Advisor: Adrian Ioana

### June 4, 2014

### 3:00 PM

### AP&M 6402

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