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I am an Associate Professor at the University of Virginia, where I've been since 2017. 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.

See here for a summary of my research. 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.

I am currently supervising two PhD students, Felipe Flores, and Aoran Wu. I am also advising James Harbour in undergraduate research. I lalso currently have one postdoc, Jacob Campbell.

I have supervised one PhD, by Mat Turnanksy. I previously supervised one distinguised major, Yichen Ma.

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