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
March 9: Wilfrid Gangbo: Optimal control problems in non-commutative variables
(UCLA)
We review the classical Mean Field Games theory and the Mean Field Games master equation, to motivate the study of optimal control problems where the observables are non-commuting self-adjoint operators. Under certain convexity assumptions, we show that the value of the optimal control problems in the non-commutative setting, describes the large-n limit of control problems on tuples of self-adjoint matrices. The classical master equation is a non-local equation of hyperbolic type whose studies were completed only under stringent assumptions on the data. Well-posedness of a “free master equation” remains an unexplored direction of research.
This talk is based on works in collaboration with Jekel-Nam-Palmer and Mou-Meszaros-Zhang.
March 16: Yasuyuki Kawahigashi: Subfactors and tensor categories in condensed matter physics
(Tokyo University)
Tensor categories have been playing more and more important roles in various fields of mathematical physics. In this talk, I will present their recent emergence in two-dimensional topological order and compare physical results using 4-tensors and technique of connections in subfactor theory. It is clear that they are similar, but I will give their precise relations, particularly through studies of the zipper condition in mathematical physics, the usual pentagon relation in tensor categories and the flat part of a connection in subfactor theory.
April 6: David Gao: Non-isomorphism of reduced free group C*-algebras, via non-K-theoretic methods.
(UCSD)
Using a new, non-K-theoretic approach involving embedding spaces in II1 factors with plenty of freely independent Haar unitaries, we prove that the reduced free group C*-algebras for different numbers of free generators are pairwise non-isomorphic. This recovers the seminal result of Pimsner and Voiculescu with a short new proof.
This talk is based on joint work with Srivatsav Kunnawalkam Elayavalli.
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.