Relativistic quantum mechanics and biomathematics. Quantum randon walks, phase space description of quantum mechanics relativistic localisation, coherent states, Wigner distribution functions.
Quantum Information, Mathematical Physics.
The theory of Lie superalgebras and the associated quantum groups, and applications thereof, e.g. exactly solvable models in statistical mechanics and knot theory. Inegrable quantum systems, quantum chemistry.
Dynamical Systems and Chaos, Hamiltonian Dynamics, Semi-classical approximations to Bose Einstein Condensates and Coupled Oscillators.
Quantum algebras, superagebras, category theory.
Exactly solvable and integrable Bose-Einstein condensates and BCS model
The representation theory of quantum algebras and superalgebras, applications in knot theory, applications in the study of integrable models of correlated electrons including impurity models, and algebraic Bethe ansatz techniques. Category theory, Bose--Einstein condensates, BCS model, quantum information theory.
Superintegrable and exactly solvable systems, supersymmetric quantum mechanics, Painleve transcendents, polynomial algebras, algebraic Bethe ansatz techniques, quantum inverse scattering method and integrable BCS models.
Exactly soluble models relevant to the theory of electronic materials: including strongly correlated electron models, quantum phase transitions in random systems and mesoscopic electronics.
Quantum optics, atom optics and laser physics, quantum mechanics and quantum measurement theory, chaos in classical and quantum systems, quantum and classical stochastic processes, the physics of information and computing and quantum noise in mesoscopic electronics.
Conformal field theory, diagram algebras, Lie algebras, representation theory, statistical mechanics, integrable systems, lattice models, polymers and percolation, string theory, black holes.
Elliptic quantum (super) groups, quantum affine (super) algebras, representation theory, q-vertex operators, algebraic analysis; non-linear integrable systems, exactly solvable models, strongly correlated fermion systems, statistical mechanics; quantum field theory, supersymmetry, conformal field theory and anomalies in gauge theory theory, correlation functions, disordered systems.
Elliptic quantum (super) groups, quantum affine (super) algebras, representation theory.