The underlying focus of mathematical analysis is the study of functions. An enormous number of the mathematical models that have been developed over the years to study the economic, physical, natural and social sciences describe the behaviour of real-world systems using functions to represent the objects being modelled, and the ways in which these objects evolve and interact is represented by equations involving functions, such as ordinary and partial differential equations. Some of these (especially nonlinear equations) are too complex to be solved using current technology, and we do not know, for instance, whether initially smooth solutions to the equations of fluid flow can develop turbulent behaviour. The members of the analysis group study equations involving functions, and in some cases, study the properties of functions and ways in which they can be represented, in order to improve our capacity to tackle the equations.

For more information, please see the Analysis at Birmingham page.

The research interests of the members of the group are given below.

Professor Jonathan Bennett


Jonathan’s interests lie in multivariable Euclidean harmonic analysis and its interactions with problems in geometric analysis and combinatorics. Recently he has been investigating the scope of heat-flow methods and induction-on-scales arguments in the analysis of geometric inequalities arising in the restriction theory for the Fourier transform.  Of particular interest to Jonathan are the many ways in which oscillatory phenomena, such as bounds on oscillatory integral operators, are governed by underlying geometric notions such as curvature or transversality.


Dr Chris Good


Recently Chris has been working on:

  • The structure of ω-limit sets of tent maps and shifts of finite type using a mixture of analytic and symbolic techniques.
  • The relationship between shadowing and expansivity of maps on compact metric spaces.
  • The role of periodic points in chaos.
  • Abstract dynamical systems modelled by compact Hausdorff spaces, separable metric spaces, the space of rational numbers and continua.
  • Characterisations of ordinals.


Dr Olga Maleva 

Senior Lecturer

Olga's research concerns differentiability of Lipschitz mappings between finite - and infinite - dimensional spaces and the geometry of exceptional sets. Recently she has been working on establishing finer properties of Universal differentiability sets and the behaviour of typical Lipschitz functions.

Olga has published research papers in leading mathematical journals and has been awarded research grants by the European Commission, the Engineering and Physical Sciences Research Council (EPSRC)  and the Royal Society. Her current research is supported by a grant from the EPSRC. At the moment, she is supervising a postdoctoral advisee and a doctoral student.

Olga has been invited speaker to a number of international research conferences and has given numerous research seminars in the UK and abroad and a series of lectures at the Summer School organised by the London Mathematical Society for the best UK undergraduates.


Dr Andrew Morris


Andrew’s research concerns the development of modern techniques in harmonic analysis, functional calculus and geometric measure theory for application to partial differential equations on Riemannian manifolds and rough domains. This includes elliptic systems with rough coefficients, local T(b) techniques, first-order methods, quadratic estimates, holomorphic functional calculus, singular integral theory, layer potentials, Hardy spaces, boundary value problems and uniform rectifiability.


Dr Susana Gutierrez


Susana has Susana’s research concerns the rigourous analytical study of qualitative and quantitative properties of partial
differential equations motivated by models of well-known physical processes. A recurring theme in her research is the application of techniques and perspectives from euclidean harmonic analysis and dispersive PDEs.

Susana has worked on developing the theory of singularity formation phenomena in the setting of nonlinear Schrodinger equations and intimately related geometric flows. These include the so-called Localised Induction Approximation for the evolution of vortex filaments in classical fluids, and more recently the family of Landau-Lifshitz-Gilbert equations describing the dynamics for the spin in ferromagnetic materials.  Susana has also contributed to the understanding of the properties of kinetic transport equations and certain nonlinear kinetic models of chemotaxis.


Dr Alessio Martini


Alessio's main area of research is harmonic analysis on Lie groups and their homogeneous spaces. This area is characterised by a strong interplay between techniques of functional analysis and Euclidean harmonic analysis and results from algebra and representation theory. Alessio has worked on uncertainty inequalities and on spectral theory for commuting systems of differential operators. Recently he has been focusing on the problem of obtaining sharp spectral multiplier theorems for non-elliptic hypoelliptic operators, such as sublaplacians, which arise naturally in non-commutative contexts.


Dr Maria Carmen Reguera

Birmingham Fellow

Maria works on harmonic analysis and especially on the theory of weighted inequalities for singular integral operators. She is also interested in related questions in operator theory for Bergman spaces and geometric analysis.