I will speak on work, joint with David Jekel and Srivatsav Kunnawalkam Elayavalli. In it, we show various new structural properties of free group factors using the recent resolution (due independently to Belinschi-Capitaine and Bordenave-Collins) of the Peterson-Thom conjecture. These results include the resolution to the coarseness conjecture independently due to the first-named author and Popa, a generalization of Ozawa-Popa's celebrated strong solidity result using vastly more general versions of the normalizer (and in an ultraproduct setting), a dichotomy result for intertwining of maximal amenable subalgebras of interpolated free group factors, as well as application to ultraproduct embeddings of nonamenable subalgebras of interpolated free group factor.

Bio: Ben Hayes is an American mathematician. He earned his doctorate from the University of California, Los Angeles in 2014. He then held a postdoc position at Vanderbilt University from 2014-2017. Since 2017, he has been a professor at the University of Virginia. His research is focused on ergodic theory (particularly sofic entropy and algebraic actions), sofic groups, measurable equivalence relations, and free entropy theory (particularly with connections to random matrices).