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 Konstantinos Dareiotis

Dr Dareiotis’ research is focused on stochastic analysis and partial differential equations (PDEs).

In particular, this includes:

• Non-linear  Degenerate Stochastic PDEs  arising as scaling limits of interacting particle systems;
• Stochastic PDEs and Integro-PDEs related to non-linear filtering;
• Diffusion processes and elliptic/parabolic PDEs;
• Regularization by noise.

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

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.

Dr Kasia Wyczesany

Dr Wyczesany’s work focuses primarily on Asymptotic Geometric Analysis. In particular, she studies high-dimensional convex sets, their asymptotic behaviour as the dimension tends to infinity, as well as their functional counterparts. This field lies at the interface of functional analysis and convex geometry and employs aspects of optimal transport theory, probability theory, combinatorics, and harmonic analysis.”

Other members include:

• Retired staff: Professor HG Dales, Professor EC Lance, Professor JR Partington, Dr DL Salinger, and Professor NJ Young.

Research seminars

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

PhD opportunities

Find out more about opportunities for prospective postgraduate researchers.