Research Activity

Mathematical physics encompasses a wide variety of topics that interface with disciplines in pure mathematics. What they have in common is that they are motivated by a desire to contribute to the understanding of phenomena arising in physics using mathematics - algebra, analysis, geometry, topology, probability, the theory of differential equations and more.

Research in our group focusses, in particular, on the following areas

• Quantum theory and partial differential equations. Spectral and other mathematical properties of differential operators arising in quantum mechanics, in particular, Schrodinger and Dirac type operators.
• Algebraic and geometric structures. Noncommutative algebraic and geometric structures, such as quantum analogues of classical Lie-theoretic objects, for founding new theories.
• Conformal Field Theory. Mathematically rigorous conformal quantum field theory, in particular, the operator algebraic frameworks of algebraic quantum field theory, and vertex operator algebras.
• Quantum theory of open systems. The mathematics of irreversible quantum dynamics, in particular dilation to reversible dynamics via operator algebraic and quantum stochastic means. Open systems arise in quantum computing, decoherence and control theory.
• Quantum probability and quantum symmetry. Quantum stochastic processes, in particular, Levy processes on (locally) compact quantum groups.

Members of the group are also affiliated with the LMS network Algebraic Quantum Field Theory in the UK.