## Mathematical Physics and Operator Algebras

•  Ben Hayes, University of Virginia
•  A random matrix approach to the Peterson-Thom conjecture
•  11/09/2020
•  3:30 PM - 4:20 PM
•  Online (virtual meeting) (Virtual Meeting Link)
•  Brent Nelson (banelson@msu.edu)

The Peterson-Thom conjecture asserts that any diffuse, amenable subalgebra of a free group factor is contained in a unique maximal amenable subalgebra. This conjecture is motivated by related results in Popa's deformation/rigidity theory and Peterson-Thom's results on $L^{2}$-Betti numbers. We present an approach to this conjecture in terms of so-called strong convergence of random matrices by formulating a conjecture which is a natural generalization of the Haagerup-Thorbjornsen theorem whose validity would imply the Peterson-Thom conjecture. This random matrix conjecture is related to recent work of Collins-Guionnet-Parraud.

## Contact

Department of Mathematics
Michigan State University