# Analysis

Analysis is one of the cornerstones of modern mathematics. It is the study of spaces and functions which have a notion of "distance" which allows limiting processes to be studied. On a basic level analysis provides the rigorous foundation of calculus and integration theory. On a more advanced level it is the main tool in the treatment of partial differential equation and stochastic processes. Modern number theory and differential geometry also tend to have serious analytical components. Analysis at Leeds centres around functional analysis, partial differential equations, geometric analysis, and harmonic analysis, both in the abstract theory, and in applications to mathematical physics and engineering.

### Dr Vladimir Kisil

Dr Vladimir Kisil studies applications of groups and their representations. It is fascinating to discover the same symmetry behind seemingly unrelated phenomena in geometry, analysis and physics.

This includes in particular:

- 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 coherant states, wavelet transform and group representations in quantum mechanics, combinatronics, etc.

### Professor Jonathan Partington

Professor Partington’s 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. He is interested in applications of operator theory, which include the study of linear semigroup systems, control theory and partial differential equations.

### Dr Ben Sharp

Dr Sharp’s research interests include geometric analysis, partial differential equations, and the calculus of variations and differential geometry. In particular the analytical study of geometric variational problems arising in pure mathematics and mathematical physics.

### Professor Alexander Strohmaier

Professor Strohmaier’s 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. He is also interested in applications in physics, in particular quantum physics, number theory, and geometry.

### Professor Nicholas Young

Professor Young’s interests include:

- 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 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.

### Research seminars

All upcoming analysis and applications seminars can be found in our events section. We are also involved with the North British Functional Analysis Seminar.

### PhD opportunities

We have opportunities for prospective postgraduate researchers. Find out more.