The Analysis and Probability group works in a wide range of areas of analysis, probability and their interface. An indication of the range may be gleaned from the list below. Some members are also involved in activities of the other research groups in the Department.

• Noncommutative Probability, including quantum and free probability
• Random Matrices and Permutations
• Operator Algebras, including nonselfadjoint algebras, and Operator Spaces
• Banach Algebras and Banach Spaces
• Abstract Harmonic Analysis and Quantum Groups
• Operator Theory and Semigroup Theory
• Algebraic Quantum Field Theory
• PDEs in Mathematical Physics, including Schrodinger and Dirac operators
• Geometric Scaling Limits of Stochastic Processes
• Stochastic Processes, Large Deviations and Heavy Tail Phenomena
• Applied Probability, MCMC
• Stochastic Approximation

We are active in several Research Networks, including:

• Quantum groups, operators and non-commutative probability research (QOP), a collaboration between Lancaster, Leeds and IMPAN Warsaw
• the North British Functional Analysis Seminar (NBFAS), which has thirteen institutional members