Work

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

Year: 2025

Type: article

Abstract: 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.

Source: Analysis & PDE

DOI: 10.2140/apde.2025.18.1805

Authors: Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli

Institutions: University of Virginia, University of Copenhagen, Princeton University, University of California San Diego

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: National Science Foundation

Awards: PostDoctoral Research Fellowship, Entropy Theory Methods in von Neumann Algebras