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
Summer Break: The POAS is on summer break from June 23 until August 17, 2026.
August 17: Dimitri Shlyakhtenko: A free analog of Bobkov’s isoperimetry inequality
(UCLA)
We prove a one-variable functional inequality which is the free probability analog of Bobkov’s isoperimetry inequality. The inequality involves the L1 norm of the difference quotient of a function f and can be viewed as a non-local isoperimetric inequality. We also prove related inequalities for subsets of an interval as well as subsets of roots of Hermite polynomials. This paper is also an experiment in AI-based exploration of free analogs of classical probability statements.
August 24: Enli Chen: Strongly convergent matrix models for q-Gaussian families
(TU Delft)
Let (s_1^{(q)}, \dots, s_r^{(q)}) be a finite q-Gaussian family. We construct explicit finite-dimensional random matrix models that converge strongly to this family for |q| < \sqrt{2} – 1 . Thus, for every noncommutative polynomial evaluated at the random matrix models, both its normalized trace and its operator norm
converge to the corresponding quantities for the q-Gaussian family in probability. The construction combines two ingredients. First, we consider normalized sums of graph-product semicircular variables indexed by Erdos-Renyi random graphs with an additional Clifford twist when q < 0. We prove quantitative operator-norm estimates for the resulting approximate q-Toeplitz relations, as well as an asymptotically sharp degree-one Khintchine inequality. In particular, the normalized
semicircular sum has limiting norm \frac{2}{\sqrt{1-q}} , which is the norm of the standard q-Gaussian variable. Using ultraproduct methods, we upgrade these estimates to complete multivariable strong convergence. Second, we use a refined tensor-GUE strong-convergence theorem to transfer these operator models to finite-dimensional random matrices. A key feature is uniformity for bounded-degree polynomials with matrix coefficients whose dimensions may grow beyond the size of the random matrices. As operator-algebraic consequences, in the above range of q, the associated q-Gaussian C^*-algebras are MF and, when there are at least two generators, their Brown-Douglas-Fillmore extension semigroups are not groups. This talk is based on recent joint work with Martijn Caspers.
September 21: Paola Zurlo: Fermionic optimal transport
(Universita degli Studi Aldo Moro, Bari)
We consider optimal transport between quantum dynamical systems on \mathbb{Z}_2– graded von Neumann algebras. In the usual, non-graded setting, Wasserstein distances between quantum systems can be defined in terms of transport plans on tensor products involving the commutant of one of the algebras. We briefly recall this construction and describe its extension to the graded setting, where the usual commutant and tensor product are replaced by the twisted commutant and the Fermi tensor product. The main point of the construction is a correspondence between fermionic and usual transport plans. More precisely, using cyclic representations associated with transport plans and the Klein isomorphisms induced by the gradings, we establish a one-to-one correspondence between fermionic transport plans and graded transport plans in the usual tensor product. This correspondence allows the Wasserstein distances in the fermionic setting to be related to the corresponding distances in the non-graded setting, and in particular yields their metric properties.