Consequences of the random matrix solution to the Peterson–Thom conjecture

We show various new structural properties of free group factors using the recent resolution (due independently to Belinschi and Capitaine, and Bordenave and Collins) of the Peterson-Thom conjecture.These results include the resolution to the coarseness conjecture due independently to the first author and Popa, a generalization of Ozawa and 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 applications to ultraproduct embeddings of nonamenable subalgebras of interpolated free group factors.