I will speak on joint work with Srivatsav Kunnawalkam Elayavalli. In it, we exhibit for every non amenable group that is initially sub-amenable (sometimes also referred to as LEA), two sofic approximations that are not conjugate by any automorphism of the universal sofic group. This addresses a question of Paunescu and generalizes the Kerr-Li, Elek-Szabo uniqueness theorem for sofic approximations.

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 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).