Analysis is the study of spaces and functions which have a notion of 'distance' which allows limiting processes to be studied. Analysis at Leeds centres around functional analysis, operator theory, and harmonic analysis, both in the abstract theory, and in applications to mathematical physics and engineering.
Our main research areas can be categorised by researcher.
My research interests are:
- Operator and C*-algebras with symmetries, particularly algebra of convolutions and pseudodifferential operators on Lie groups and homogeneous spaces
- Functional calculus of operators and associated notions of (joint) spectrum of operators
- Hilbert spaces of analytic functions with reproducing kernels arising from group representations in complex and Clifford analysis
- Applications of coherent states, wavelet transform and group representations in quantum mechanics, combinatorics, etc.
My research interests centre on operator theory and Banach spaces of analytic functions. These include very abstract questions about invariant subspaces, where tools from complex analysis have been found useful, and also the study of particular types of operator, such as Hankel, Toeplitz and composition operators. I am very interested in applications of operator theory, which include the study of linear semigroup systems, control theory and partial differential equations.
My research is mainly in the analysis of partial differential operators. This includes spectral theory of elliptic partial differential operators on manifolds, scattering theory, parametrix constructions, index theory for elliptic and non-elliptic operators, Fourier- and pseudo-differential operators. I am also interested in applications in physics, in particular quantum physics, number theory, and geometry.
My research interests are in mathematical analysis, particularly operators on Hilbert space; complex analysis; H infinity control. Recent work, in collaboration with Jim Agler (UC San Diego) and John E. McCarthy (Washington University), is on the extension of some classical theorems of function theory to functions of two variables.
Visit our analysis research group website.
All upcoming seminars can be found in our events section.
We have opportunities for prospective PhD students. Potential projects can be found in our postgraduate research opportunities directory.