Description of the ERC Advanced Grant NCDFP


Type of grant: 
ERC Advanced Grant 
Title: 
NonCommutative Distributions in Free Probability 
Funded by: 
European Research Council 
Principal Investigator: 
Roland Speicher 
Duration: 
1 February 2014  31 January 2019 
Aim: 
The aim of the grant is to study new directions in free probability theory with
high potential to lead to breakthroughs in our understanding of random matrix models
and operator algebras. We will drive forward the study of free analysis which is intended to provide a whole new mathematical theory for variables with the highest degree of noncommutativity and which lies at the crossroad of many exciting mathematical subjects. More specifically, the objective of the research founded by this grant is to extend our armory for dealing with noncommutative distributions and to attack some of the fundamental problems which are related to such distributions, like: the existence and properties of the limit of multimatrix models; the isomorphism problem for free group factors, and more generally, properties of free entropy and free entropy dimension as invariants for von Neumann algebras. 
Components of the research supported by the ERC Advanced Grant NCDFP
Quantum Symmetries: 
The first project deals with quantum symmetries of noncommutative distributions. We try to classify noncommutative symmetries and describe the effect of invariance under
such quantum symmetries for noncommutative distributions. This is based on the theory of easy quantum groups. Details 
Free Malliavin Calculus: 
In the second project we will develop the theory of free Malliavin calculus. This will then be used to investigate regularity properties of noncommutative distributions. Details 
Analytic Aspects of OperatorValued Free Probability: 
In the third project, we will study the analytic theory of operatorvalued free convolutions. One specific goal in this context is to find and implement algorithms for calculating noncommutative distributions and asymptotic eigenvalue distributions for general random matrix problems. Details 
Updated: 23 September 2013 Moritz Weber  Impressum 