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arXiv · 2308.14109

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

Ben Hayes·David Jekel·Srivatsav Kunnawalkam Elayavalli
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Abstract

In this paper 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 factors.

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Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli. 2024-07-26. Consequences of the random matrix solution to the Peterson-Thom conjecture. https://doi.org/10.2140/apde.2025.18.1805

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