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Consequences of the
random matrix solution to the Peterson–Thom conjecture
Ben Hayes, David Jekel and Srivatsav Kunnawalkam Elayavalli |
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Vol. 18 (2025), No. 7, 1805–1834
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Abstract |
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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. |
Keywords
free group factors, 1-bounded entropy, anti-coarse space,
coarseness conjecture
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Mathematical Subject Classification
Primary: 46L09, 46L53, 46L54
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Milestones
Received: 8 December 2023
Accepted: 20 July 2024
Published: 13 June 2025
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Authors |
| Ben Hayes | |
| Department of Mathematics University of Virginia Charlottesville, VA United States |
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| David Jekel | |
| Department of Mathematics University of Copenhagen Copenhagen Denmark |
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| Srivatsav Kunnawalkam Elayavalli | |
| Department of Mathematics University of California, San Diego La Jolla, CA United States |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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