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 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 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 interested in applications of operator theory, which include the study of linear semigroup systems, control theory and partial differential equations.
- Geometric analysis, partial differential equations, the calculus of variations and differential geometry. In particular the analytical study of geometric variational problems arising in pure mathematics and mathematical physics.
- 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.
- 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.
Other members of our group include:
- Academic staff: Dr A Ghaani Farashahi, Dr Florian Hanisch
- Visiting staff: Professor ATM Lau, Dr Eskil Rydhe, Dr D Strauss
- Retired staff: Professor HG Dales, Professor EC Lance, Dr DL Salinger
- Postgraduate researchers: Khairiah Alahmari, Amerah Alameer, Asmahan Alajyan, Amjad Alghamdi, Fadhel Almalki, Taghreed Alqurashi, Dale Hodgson, Onirban Islam, Ryan O'Loughlin, Shuang Zheng.
- Young Functional Analysts' Workshop, 3-5 April 2019
- Fredholm theory of non-elliptic operators, 3-7 June 2019
We have opportunities for prospective postgraduate researchers. Find out more.