A random matrix approach to the Peterson-Thom conjecture
Ben Hayes
Abstract
The Peterson-Thom conjecture asserts that any diffuse, amenable subalgebra of a free group factor is contained in a unique maximal amenable subalgebra.This conjecture is motivated by related results in Popa's deformation/rigidity theory and Peterson-Thom's results on L 2 -Betti numbers.We present an approach to this conjecture in terms of so-called strong convergence of random matrices by formulating a conjecture which is a natural generalization of the Haagerup-Thorbjørnsen theorem whose validity would imply the Peterson-Thom conjecture.This random matrix conjecture is related to recent work of Collins-Guionnet-Parraud.
Topics & Concepts
MathematicsConjectureRandom matrixMatrix (chemical analysis)Pure mathematicsAlgebra over a fieldApplied mathematicsEigenvalues and eigenvectorsPhysicsMaterials scienceComposite materialQuantum mechanicsAdvanced Operator Algebra ResearchRandom Matrices and ApplicationsAlgebraic structures and combinatorial models