Mathematical Physics

Cardiff has an expanding research group in mathematical physics accumulating an expertise that is unique in the UK. The group consists of R. Behrend, D. E. Evans, as well as S. Hollands who has joined the group recently.

Our interests sweep a broad range of topics, from pure mathematics to theoretical physics. On the pure mathematics side, we are interested in questions related to operator algebras, K-theory, quantum groups, geometry, analysis and topology. On the physics side, we are interested in quantum field theory, statistical mechanics, gravitation and integrable systems. There are many striking and profound relations between many of these ideas from mathematics and physics, and not surprisingly, these have had a deep influence on each other in recent years.

Our own specific interests include:

Key Research Areas

Pure Mathematics

• Operator algebras and non-commutative geometry
• K-theory (including twisted and equivariant versions), Elliott programme,  and non-commutative dynamical systems.
• Quantum symmetries : subfactors, tensor categories, Hopf algebras, quantum groups;
• paragroups, Q-systems, lambda-lattices, planar algebras
• Enumerative Combinatorics
• Modular invariants, subfactors

Mathematical and Theoretical Physics

• Foundations and constructive approaches to quantum field theory (algebraic approach, conformal field theories including boundaries, curved backgrounds, perturbation theory, topological field theories)
• Classical general relativity (Asymptotic charges, Hamiltonian formalism, black holes, AdS-CFT)
• Statistical Mechanics: classical and quantum, equilibrium and non-equilibrium, integrable systems

Seminars

Seminars

Event	Day and time	Room
Group Seminar	Thursday 15:00	M/2.06
Student Seminar	Wednesday Biweekly 15:00	M/2.06

 

International Collaborations

The members of our group work together with groups from:

• University of Alberta (CA)
• University of Copenhagen (DK)
• ANU Canberra (AUS)
• University of Chicago (USA)http://physics.uchicago.edu/t_rel.html
• Göttingen University (FRG) http://www.lqp.uni-goettingen.de/
• Harvard (USA) http://www.arthurjaffe.com/
• Hamburg University (FRG) http://unith.desy.de/research/aqft
• UC Santa Barbara (USA) http://www.physics.ucsb.edu/~relativity/
• ETH Zurich (CH) http://www.itp.phys.ethz.ch/mathphys/
• Universidade de Sao Paulo (BR) http://fma.if.usp.br/