About
The Probabilistic Operator Algebras Seminar (POAS) is an online seminar organized by Dan-Virgil Voiculescu that features talks on recent advances in free probability, operator algebras, random matrices, and related topics. It meets usually weekly from 9:00-10:30am Pacific time. This site is managed by David Jekel. Please contact [email protected] for more information or to be added to the email list.
Upcoming Talks
April 20: Zachary Stier: Finite free information inequalities
(UC Berkeley)
We establish the finite free analogue to the classical and free Stam inequality, proved via a novel connection between the Jacobian of the finite free convolution map and the score vector (the finite free analogue of the Hilbert transform). Time permitting, we will then discuss using the same technique to prove monotonicity of the finite free Fisher information; applications to finite free entropy monotonicity; and obtaining a result of Shlyakhtenko and Tao in free probability as a limiting instance.
Reference: arXiv:2602.15822; joint work with Jorge Garza-Vargas and Nikhil Srivastava.
April 27: Guillaume Cébron: Functional inequalities for Boolean entropy
(University of Toulouse)
I will describe a Boolean information-theoretic framework paralleling the classical and free settings, by introducing Microstates and Non-Microstates Boolean Fisher informations and relating them to Boolean entropy through Bruijn-type identities. We established Boolean analogues of the main functional inequalities, including logarithmic Sobolev, HWI, HSI, Talagrand and WSH-type inequalities. It yields new quantitative Berry-Esseen bounds and entropic convergence rates in the Boolean CLT.
Reference: arXiv.2602.23527; joint work with Kewei Pan.
May 4: Magdalena Musat and Mikael Rørdam: Tensor products of convex compact sets and entanglement in C*-algebras
(University of Copenhagen)
The Namioka-Phelps tensor product of two convex compact sets associates two new compact convex sets: the minimal and the maximal tensor product where the former is contained in the latter. They show that the two tensor products agree if one of the two convex compact sets is a Choquet simplex. It remains an open problem, known as Barker’s conjecture, if the converse also holds. Barker’s conjecture was recently verified by Aubrun-Lami-Palazuelos-Plavala in the finite dimensional case (and was verified by Namioka and Phelps when one of the two convex compact sets is the square).
We show that Barker’s conjecture holds when the compact convex sets are state spaces of \mathrm{C}^*– algebras, and we describe the two Namioka-Phelps tensor products. The minimal tensor product is precisely the set of entangled states in the (minimal) tensor product of the \mathrm{C}^*-algebras, and one can describe the maximal tensor product in terms of positive maps. We identify the trace space of
the tensor product of \mathrm{C}^*-algebras as the Namioka-Phelps tensor product of the trace spaces and use this to say when the trace simplex of a tensor product of \mathrm{C}^*-algebras is the Poulsen simplex.
May 4: Otte Heinävaara: Convolution comparison measures
(Caltech)
We introduce a new functional comparison between classical and free convolutions the expectation of function f with respect to classical convolution (of two compactly supported probability measures) is larger than the expectation with respect to free convolution, as long as the fourth derivative of f is non-negative. The comparison is based on the existence of convolution comparison measures, novel measures on the plane whose positivity depends on a peculiar identity involving Hermitian matrices.