Analysis 

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

Professor

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.

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Dr Hong Duong

Lecturer

Hong Duong is a Lecturer in Mathematical/Statistics. His research interests lie in the intersections of analysis and applied probability. Most of his research are inspired from applications in molecular dynamics, material sciences and biological systems.

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Professor Chris Good

Reader

Recently Chris has been working on:

  • Characterizations of maps with the shadowing property.
  • Dynamical systems with a topological rather than metric phase space.
  • The Ausalnder-Yorke dichotomy, equicontinuity, transitivity and sensitivity.
  • Countable dynamical systems.
  • Induced dynamics on hypeerspaces and function spaces.
  • Coarse graining of complex systems.

For a complete list of Chris’s publications and links to copies of his papers, please follow the link below:

Professor Chris Good's publications and citations (PDF)

For more information about Chris, please visit his staff profile:

Professor Chris Good staff profile

Dr Olga Maleva 

Reader in Pure Mathematics

Olga's research concerns differentiability of Lipschitz mappings between finite - and infinite - dimensional spaces and the geometry of exceptional sets. Olga is particularly interested in a range of topics related to the converse to the classical theorem of Rademacher. Namely, she has been working on establishing finer measure-theoretic regularity properties (such as porosity, rectifiability, Hausdorff/Minkowski dimensions etc) of Universal differentiability sets and sets on which Lipschitz mappings behave in the worst possible way, as well as 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.

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Dr Andrew Morris

Lecturer

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.

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Dr Susana Gutierrez

Lecturer

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.

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Dr Alessio Martini

Lecturer

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.

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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.

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Dr Tony Samuel

Lecturer

Tony Samuel is a Lecturer in Mathematics and Statistics at the University of Birmingham. His research interests include aperiodic order, Diophantine approximations, dynamical systems (symbolic and measure preserving), ergodic theory (finite and infinite), geometry (fractal, hyperbolic and non-commutative) and potential theory. Recently, his focus has been on applications of ergodic theory, non-commutative geometry and potential theory to fractals and quasi-crystals. He is also very interested in linking these topics to other areas of mathematics, such as, geometric group theory, geometric measure theory and renewal theory.

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Dr Diogo Oliveira e Silva

Lecturer

Diogo is broadly interested in Mathematical Analysis. His research focuses on Euclidean Harmonic Analysis with special emphasis on sharp inequalities, oscillatory integrals and restriction theory for the Fourier transform. More recently Diogo became interested in Uncertainty Principles, Sphere Packings and Nonlinear Fourier Analysis. 

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Dr Yuzhao Wang

Lecturer

Yuzhao’s primary research area is mathematical analysis of nonlinear dispersive partial differential equations (PDEs), with tools from harmonic analysis, probability theory, and dynamical systems. In particular, he is interested in Strichartz estimates and its applications to dispersive nonlinear PDEs, probabilistic aspects of nonlinear dispersive PDEs, and normal form method applied to nonlinear dispersive PDEs. 

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Dr Jingyu Huang

Lecturer

Dr Jingyu Huang primary areas of research involve stochastic analysis and stochastic partial differential equations.

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Dr John Meyer

Lecturer

Dr John Meyer is a Lecturer of Applied Mathematics. His research is in the field of analysis of nonlinear differential equations and is interested in the following areas: reaction-diffusion theory, maximum principles, quasi-linear parabolic partial differential equations, chemical reaction modelling.

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