Brent Nelson

Brent Nelson is an Associate Professor in the Department of Mathematics at Michigan State University (MSU). He holds a PhD in Mathematics from the University of California, Los Angeles (UCLA), under the supervision of Dimitri Shlyakhtenko, and a BS in Mathematics from the University of Illinois at Urbana-Champaign (UIUC). His research focuses on free probability, non-tracial von Neumann algebras, free transport, subfactor planar algebras, and bi-free probability. He has held postdoctoral positions at Vanderbilt University and the University of California, Berkeley, and has been recognized with awards including the Pacific Journal of Mathematics Dissertation Prize (2015) and the Distinguished Teaching Award (2018).

Key research interests include the structure of von Neumann algebras, free monotone transport, and applications to quantum graphs and operator algebras. He has authored numerous publications in top-tier journals and presented at international conferences such as the Canadian Operator Symposium and the Banff International Research Station workshops. His teaching includes advanced courses on functional analysis, operator algebras, and real/complex analysis at MSU and other institutions.

Grants include NSF funding for projects on non-tracial derivations and distributions, and he has organized conferences like the Groundwork for Operator Algebras Lecture Series (2020). His work bridges abstract operator algebra theory with applications in quantum probability and ergodic theory.