19 May 2021

Operator algebras receives DFF-grant for research in quantum mathematics

Research

The operator algebras groups at UCPH and SDU (Odense) was granted more than 5 MDKK for the DFF (Independent Research Fund Denmark) Research project 2 ”Operator Algebras, Groups, and Quantum Spaces”.

The operator algebra group at UCPH
The operator algebra group at UCPH

The research group at our department consists of Magdalena Musat, Søren Eilers, Asger Dag Törnquist and Mikael Rørdam, the latter being in charge of the project. Two postdocs, one at UCPH and one at SDU, will be appointed by the grant.

The project concerns a circle of problem within operator algebras, a mathematical discipline within functional analysis that also can be described as quantum mathematics. The primary research objects are C*-algebras and von Neumann algebras, that encompasses non-commutativity as it appears for example in the Heisenberg uncertainty principle.

The main focus of the project is the interplay between operator algebras and adjacent fields of mathematics through three interconnected themes: classification of C*-algebras, groups & dynamical systems, and aspects of quantum metric spaces.

The project will lead to new insight into the classification theory for C*-algebras (simple and non-simple), and will bring us closer to an understanding of the connections between spectral triples from Connes' non-commutative geometry, quantum groups and quantum metric spaces and their K-theory. It will further have important applications within quantum information theory, geometric and combinatoric group theory, symbolic dynamical systems, and Borel complexity.


DFF (Independent Research Fund, Denmark) supports each year some of the most promising and original ideas across all scientific fields when the programs Research Project 1 and 2 are awarded. This year, 191 original projects were supported with 668 MDKK, of which FNU (Natural Sciences) awarded a total of 10 Research Project 2 grants.