Professor Frank Nijhoff

Profile

Teaching activities

Research interests

My main research interests are directed towards the theory of continuous and discrete integrable systems and their connections with wider areas of pure and applied mathematics and with physics. A starting point for many of my contributions has been the study of integrable lattice equations, i.e., partial difference equations on the space-time lattice which share many of the beautiful features and properties with the more well-known integrable PDEs like the famous Korteweg-de Vries (KdV) equation. The study of solutions of such parial difference equations lead to conections with many areas of mathematics: soliton theory, algebraic geometry, Hamiltonian mechanics and the theory of symmetries and conservation laws. In fact, special solutions (i.e. reductions) lead to integrable dynamical mappings, discrete Painleve equations, and discrete systems of Calogero-Moser type. Fundamentally, these systems can also be quantized, and lead to corresponding systems in a discrete version of quantum mechanics. Furthermore, the study of the Lagrangian formalism of such systems has recently led to new paradigms in the theory of variational calculus.

I'm a member of the Algebra, geometry and integrable systems research group.

Qualifications

• Doctoraat in Wiskunde en Natuurwetenschappen (Universiteit Leiden, 1984)

Professional memberships

• American Mathematical Society (AMS)
• London Mathematical Society (LMS)
• International Association of Mathematical Physics (IAMP)

Research groups and institutes

• Applied Mathematics

Current postgraduate researchers

• Duncan Sleigh
• Jacob Richardson
• Benjamin Morris