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OAFPG Report Summary

Project ID: 247321
Funded under: FP7-IDEAS-ERC
Country: Denmark

Final Report Summary - OAFPG (Operator Algebras, Free Probability, and Groups)

The main mathematical subjects covered by the project were:

(I) Approximation properties for groups and their C*- and von Neumann algebras.
(II) Research related to the still open Connes embedding problem.
(III) Free probability and random matrices.

The most important results were obtained in sections (I) and (II). Among those results are:

(a) A complete classification of the simple connected Lie groups that has the approximation property (AP), with applications to the C*- and von Neumann algebras associated with lattices in such groups.
(b) The solution of the asymptotic quantum Birkhoff conjecture, followed by the discovery of a connection between problems in quantum information theory and the famous Connes embedding problem.

The project has supported 4 Post docs and 3 PhD students. A major part of the 31 research articles, that came out of the project are joint works between the PI and the younger researchers associated to the project. The research results obtained during the time of the project has been presented by the PI and by other members of the research team at several conferences in Europe, Canada, USA, China, Japan and Korea.

In 2012, the PI received the European Latsis prize for his research in mathematics.

Reported by

Københavns Universitet
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