ERC Advanced Grant

Description of the ERC Advanced Grant NCDFP

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 non-commutativity 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 non-commutative distributions and to attack some of the fundamental problems which are related to such distributions, like: the existence and properties of the limit of multi-matrix 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.

Quantum Symmetries:
The first project deals with quantum symmetries of non-commutative distributions. We try to classify non-commutative symmetries and describe the effect of invariance under such quantum symmetries for non-commutative 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 non-commutative distributions.
Details

Analytic Aspects of Operator-Valued Free Probability:
In the third project, we will study the analytic theory of operator-valued free convolutions. One specific goal in this context is to find and implement algorithms for calculating non-commutative distributions and asymptotic eigenvalue distributions for general random matrix problems.
Details

Activities funded by the ERC Advanced Grant NCDFP

C*-Algebras, Random Matrices, Free Probability, and Beyond
Conference in honour of James A. Mingo on the occasion of his 60th birthday
partially supported by the ERC Advanced Grant NCDFP
Kingston, Canada
October 16 - 17, 2015
organized by Serban Belinschi (Toulose, France), M. Ram Murty (Kingston, Canada), Roland Speicher (Saarbrücken)

George Boole Mathematical Sciences Conference
Theme 8: Quantum Probabilistic Symmetries & Quantized Boolean Algebras
partially supported by the ERC Advanced Grant NCDFP
Cork, Ireland
August 17 - 28, 2015

Quantum Groups and Quantum Information Theory
partially supported by the ERC Advanced Grant NCDFP
Herstmonceux, UK
July 13 - 17, 2015
organized by Benoit Collins (Kyoto, Japan), James Mingo (Kingston, Canada), Ashley
Montanaro (Bristol, UK), Maria Grazia Viola (Lakehead, Canada), Moritz Weber (Saarbrücken)

Free (Stochastic) Analysis
Mini-workshop on Operator Valued Free Probability, Non-Commutative Functions
and the Functions in Several Non-Commuting Random Variables
fully funded by the ERC Advanced Grant NCDFP
Saarbrücken, Germany
23 March - 27 March, 2015
organized by Tobias Mai, Roland Speicher and John Williams (all Saarbrücken)

Special session on free probability and operator theory,
part of IWOTA 2014
partially supported by the ERC Advanced Grant NCDFP
International Workshop on Operator Theory and its Applications
yearly conference, this time held in Amsterdam, Netherlands
July 14 - 18, 2014
special session organized by Serban Belinschi (Queens, Canada), Roland Speicher
and Moritz Weber (both Saarbrücken)

Quantum Symmetries in Free Probability
Mini-workshop on easy quantum groups and other symmetries in free probability
fully funded by the ERC Advanced Grant NCDFP
Saarbrücken, Germany
31 March - 4 April, 2014
organized by Roland Speicher and Moritz Weber (both Saarbrücken)