Mathematical Analysis

at the University of Birmingham

wave front in the Heisenberg group
wave front in the Heisenberg group
The Analysis Group in the School of Mathematics conducts research in a wide variety of interconnected areas. Current strengths lie in:
sliding tubes
evolving Kakeya sets
Details of the research activities of the members of the group are given below and under Fellows and Students.
Jonathan Bennett

Jonathan Bennett Euclidean harmonic analysis

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 are governed by underlying geometric notions such as curvature or transversality.

Chris Good

Chris Good topology and topological dynamics

Chris's research is in topological dynamics and set theoretic topology. His particular interests include (in no particular order): the structure of omega-limit sets; shadowing; symbolic dynamics of tent maps; topologies making given mappings continuous; generalised metric spaces and monotonicity; Dowker spaces and normality in products; the construction of counterexamples.

Susana Gutierrez

Susana Gutierrez harmonic analysis and PDE

Susana's research focuses on the analysis of partial differential equations modelling physical processes using techniques and perspectives from harmonic analysis and dispersive PDEs. Susana has studied singularity formation phenomena for nonlinear Schrödinger equations and related geometric flows (Localized Induction Approximation and Landau-Lifshitz-Gilbert equations), as well as properties of the solutions of kinetic transport equations and nonlinear kinetic models of chemotaxis.

Olga Maleva

Olga Maleva geometric measure theory and Banach space geometry

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 and 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.

Alessio Martini

Alessio Martini harmonic analysis on Lie groups

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 and harmonic analysis and results from algebra and representation theory. Alessio has worked on uncertainty inequalities, on spectral theory for commuting differential operators and, more recently, on the problem of obtaining sharp spectral multiplier theorems for sub-elliptic operators.

Andrew Morris

Andrew Morris harmonic analysis, functional calculus and PDE

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.

Diogo Oliveira e Silva

Diogo Oliveira e Silva harmonic analysis

Diogo's research focuses on 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 and nonlinear Fourier analysis.

Maria Carmen Reguera

Maria Carmen Reguera harmonic and complex analysis

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.

Maria Carmen Reguera

Yuzhao Wang nonlinear PDE and harmonic analysis

Yuzhao's main research interests are Nonlinear Partial Differential Equations (PDEs) and Harmonic Analysis. This includes the study of nonlinear dispersive PDEs such as nonlinear Schrödinger equations, nonlinear wave equations, and the KdV equation by using techniques from PDEs, Harmonic Analysis, and Probability theory. Yuzhao investigates well-posedness (existence, uniqueness, and stability of solutions) in both deterministic and probabilistic settings, existence of invariant measures, and Strichartz estimates in different settings. He is also interested in Fourier restriction theory and l2 decoupling theory.

recent members