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I am a Tenure-Track Assistant Professor at the University of Virginia. I was an Assistant Professor (Postdoc) at Vanderbilt University for three years from 2014-2017. I earned my my PhD in June 2014 at the University of California, Los Angeles, under the direction of my doctoral advisor Dimitri Shlyakhtenko. I received my bachelor's degree in June 2009 from the University of Washington. You can find my CV here.

I did a senior thesis at University of Washington, under the supervision of Doug Lind, which you can find here. You can also find my PhD thesis here.

**Interests:**

I am interested in operator algebras and ergodic theory, in particular their intersection. I am currently investigating sofic entropy as well as microstates free entropy dimension. I try to apply techniques from operator algebras/free probability to solve problems in ergodic theory and vice versa. My initial research used ideas from sofic entropy to give a definition of extended von Neumann dimension for actions of groups/equivalence relations on L^{p}-spaces, with applications to the cost vs. l^{2}-Betti number problem. I am also interested in measured group theory, the study of sofic groups, as well as random matrices.

**Contact**

Department of Mathematics

University of Virginia

141 Cabell Drive, Kerchof Hall

P.O. Box 400137

Charlottesville, VA 22904

**E-mail:** brh5c@virginia.edu