Pure Mathematics PhD/MPhil – (Ph.D.)

Contents

Research interests of staff

* Dr Jonathan Bennett – works in analysis, particularly in the area of Euclidean harmonic analysis; most recently, has focused on developing natural multilinear analogues of the classical restriction Kakeya, and Bochner–Riesz conjectures (along with other collaborators in the UK, Spain and the US).
* Professor Robert Curtis – the sporadic simple groups and their geometries by way of symmetric presentations; research uses algebraic computer programs and has connections with geometry, combinatorics and representation theory.
* Dr Paul Flavell – investigates the structure theory of finite groups to obtain theorems that apply to the finite simple groups, but are independent of their classification; recent successes include a paper entitled 'A Hall-Higman-Shult type theorem for arbitrary groups'.
* Dr Tony Gardiner – developing a new framework for the study of imprimitive graphs.
* Dr Chris Good – works in general and set-theoretic topology (interested in generalised metric spaces, the construction of examples and the role of set-theoretic axioms on topological structures) and in dynamical systems (interested in the topological structure of invariant sets, symbolic dynamics and characterisations of continuity in abstract dynamical systems); regularly collaborates with colleagues from UK (Oxford), New Zealand and North America.
* Dr Simon Goodwin – carries out research in Lie theory: algebraic groups, finite groups of Lie type, Lie algebras, finite W-algebras
* Dr Ralf Gramlich – researches interests in geometric and topological aspects of algebraic groups and their generalisations, including finite simple groups and Kac-Moody groups (he studies these groups via their action on buildings); interested in groups acting on graphs and related combinatorial structures.
* Dr Susana Gutierrez – research interests in a variety of aspects of harmonic analysis, with particular emphasis on applications to linear and non-linear partial differential equations; recently involved in trying to understand different physical phenomena leading to singularity formation in curve flows and free boundary problems.
* Dr Corneliu Hoffman – groups and geometries; in particular, geometries called 'buildings' and the groups related to them; also interested in representations of groups and in applications of groups to number theory.
* Dr Richard Kaye – model theory, including non-standard models of arithmetic: this has connections with group theory, topology and infinite permutation groups.
* Professor Daniela Kühn and Dr Deryk Osthus – work as a team on various areas of graph theory, often involving the use of probabilistic methods, which has proved to be remarkably successful in many situations; awarded the biannual European Prize in Combinatorics (2003) for their work on extremal graph theory.
* Dr Kay Magaard – projects related to the structure and representation theory of finite simple groups, on finite groups in general and their applications; participating in the fundamental and ongoing revision of the CFSG; studies the automorphism groups of Riemann surfaces, where he computes Hurwitz-Loci of Riemann surfaces with a given automorphism group; studies black box groups, where he solves constructive recognition problems for simple Chevalley groups.
* Dr Olga Maleva - Non-linear geometric functional analysis; differentiability of Lipschitz mappings; null sets in Banach spaces; Hausdorff measures and dimensions, rectifiability; classical real analysis, derivatives and their generalisations.
* Professor Chris Parker – theorems designed to recognise simple groups from some fragment of their p-local subgroup structure: results will be of use in the ambitious programme to revise the classification of the finite simple groups (CFSG) using techniques related to the so-called 'amalgam method'.
* Professor Sergey Shpectorov – the study of groups (and in particular, finite simple groups) via the geometries these groups act on; research in several areas related to groups, such as fusion systems, inverse Galois theory, and algebraic graph theory.
* Dr Neal Bez – interests in euclidean harmonic analysis and connections to geometric analysis and partial differential equations.