Pure Mathematics

Study mode:On campus Study type:Full-time Languages: English
107 place StudyQA ranking:3635 Duration:48 months

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There are opportunities for postgraduate research in Pure Mathematics, especially in the areas of algebra, analysis, combinatorics and graph theory. Training is provided through individual supervision of research, by advanced seminar courses and conferences, and by generic courses. The PhD degree usually involves a qualifying dissertation submitted during the second year of study, which is helpful training for writing the PhD thesis.
The Pure Mathematics group contributes to research in various parts of algebra, model theory, combinatorics, set theory and analysis. Birmingham is recognised as one of the leading centres in the European Union for research in group theory.

Key facts

Type of Course: Doctoral research

Duration: PhD: 34 years full-time; MPhil: 1 year full-time; also available part-time over 2 years


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 BochnerRiesz 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.


Ensure your qualifications meet our entry requirements for research degrees

To gain admission to a research degree programme (with the exception of the Doctor of Dental Surgery (DDS) or Doctor of Medicine (MD)) an applicant must comply with the following entry requirements:

* Attainment of an Honours degree (normally a First or Upper Second Class Honours degree or equivalent) in a relevant subject awarded by an approved university, or
* Attainment of an alternative qualification or qualifications and/or evidence of experience judged by the University as indicative of an applicants potential for research and as satisfactory for the purpose of entry to a research degree programme.

In addition:

* Admission and registration for a research degree programme may be conditional on satisfactory completion of preliminary study, which may include assessment.
* In some cases you will also need to have completed a Masters degree or equivalent qualification in a relevant subject.

Please note

* Entry onto many programmes is highly competitive, therefore we consider the skills, attributes, motivation and potential for success of an individual when deciding whether to make an offer.
* Specific entry requirements are given for each programme. Any academic and professional qualifications or industrial experience you may have are normally taken into account, and in some cases form an integral part of the entrance requirements. If your qualifications are non-standard or different from the entry requirements stated in the online prospectus, please contact the relevant school or department to discuss whether your application would be considered.
* After we have received your application you may, if you live in the UK, be invited for an interview or to visit us to discuss your application.

English Language Requirements

IELTS band: 5.5 TOEFL iBT® test: 80

IMPORTANT NOTE: Since April 2014 the ETS tests (including TOEFL and TOEIC) are no longer accepted for Tier 4 visa applications to the United Kingdom. The university might still accept these tests to admit you to the university, but if you require a Tier 4 visa to enter the UK and begin your degree programme, these tests will not be sufficient to obtain your Visa.

The IELTS test is most widely accepted by universities and is also accepted for Tier 4 visas to the UK- learn more.


Scholarships and studentships We award up to ten home/EU EPSRC doctoral training grants each year to eligible students. In exceptional circumstances fully-funded School doctoral training grants may be awarded. Additional income can often be generated by tutorial and marking work.

International students can often gain funding through overseas research scholarships, Commonwealth scholarships or their home government.

See the University of Birmingham Website for more details on fees and funding.

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