Funded PhD Studentship in Algebra

Research covers key areas of algebra, geometry, mathematical physics and topology. This reaches from the study of algebras, group theory (including Lie groups/algebraic groups), Lie algebras, Hopf algebras, (higher) category theory, representation theory and homological algebra to algebraic geometry, differential and difference equations, braid groups, configuration spaces, surfaces and manifolds, and to mathematics on the interface of algebra with topology and mathematical physics, such as the pentagon equation, skew braces, (extended) topological quantum field theories, higher Lie and gauge theory, mathematical models for topological phases of matter and the ensuing paradigms for topological quantum computing. There are also strong connections to Logic, where topics such as algebraic topology, category theory, categorical and homotopical algebra, model theory, permutation groups, surreal numbers and ordered fields play a role in the interface.<br /> <br /> This is a strong and active area of research. There are many collaborations and interactions between researchers across these areas, both at Leeds and externally, and there is a thriving community of postdoctoral researchers (supported in part by a substantial EPSRC Programme Grant in combinatorial representation theory) and PhD students, as well as regular seminars in Algebra and in Mathematical Physics.<br />

<p class="MsoNoSpacing">We are delighted to offer a fully funded PhD project and applications are invited from strongly motivated and academically excellent candidates for fully funded PhD study in Algebra, within these strategic priority Research areas:</p> <p><strong>Oleg Chalykh</strong>: Quivers and their representations; Moduli spaces in representation theory and mathematical physics; Cherednik algebras and double affine Hecke algebras. Please contact Dr Chalykh by email to <strong><a href="mailto:o.chalykh@leeds.ac.uk">o.chalykh@leeds.ac.uk</a></strong></p> <p><a href="https://eps.leeds.ac.uk/maths/staff/14917/dr-ilaria-colazzo"><strong>Ilaria Colazzo</strong></a>: Algebraic structures connected with combinatorial solutions of the Yang-Baxter equation and Pentagon equation. Please contact Dr Colazzo by email to <strong><a href="mailto:I.Colazzo@leeds.ac.uk">I.Colazzo@leeds.ac.uk</a></strong></p> <p><a href="https://eps.leeds.ac.uk/maths/staff/4061/professor-paul-martin"><strong>Paul Martin</strong></a>: Algebras and computation for statistical mechanics; combinatorial and geometric algebra in the interface of mathematics with physics. Please contact Professor Martin by email to <strong><a href="mailto:P.P.Martin@leeds.ac.uk">P.P.Martin@leeds.ac.uk</a></strong></p> <p><a href="https://eps.leeds.ac.uk/maths/staff/4021/dr-joao-faria-martins"><strong>Joao Faria Martins</strong></a>: (Extended) topological quantum field theories; Hopf algebras and low dimensional topology; Algebraic models for homotopy types. Please contact Dr Faria Martins by email to <strong><a href="mailto:J.FariaMartins@leeds.ac.uk">J.FariaMartins@leeds.ac.uk</a></strong></p> <p><a href="https://eps.leeds.ac.uk/maths/staff/4083/dr-rudolf-tange"><strong>Rudolf Tange</strong></a>: Representations, invariants and actions of reductive algebraic groups in characteristic p. Please contact Dr Tange by email to <strong><a href="mailto:R.H.Tange@leeds.ac.uk">R.H.Tange@leeds.ac.uk</a></strong></p> <p><a href="https://eps.leeds.ac.uk/maths/staff/15258/dr-f-tripaldi"><strong>Francesca Tripaldi</strong></a>: Spectral sequences on nilpotent Lie groups, homotopy transfer theorem on homogeneous Lie groups, Lie algebra cohomology of nilpotent Lie groups. Please contact Dr Tripaldi by email to <strong><a href="mailto:F.Tripaldi@leeds.ac.uk">F.Tripaldi@leeds.ac.uk</a></strong></p> <p><a href="https://eps.leeds.ac.uk/maths/staff/14204/dr-michael-wibmer"><strong>Michael Wibmer</strong></a>: Differential Galois theory; Difference algebraic groups. Please contact Dr Wibmer by email to<strong> <a href="mailto:M.Wibmer@leeds.ac.uk">M.Wibmer@leeds.ac.uk</a></strong></p>

<p>Formal applications for research degree study should be made online through the <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University's website</a>. Please state clearly in the Planned Course of Study section that you are applying for <em><strong>EPSRC DTP Engineering & Physical Sciences</strong></em> and in the research information section that the research degree you wish to be considered for is <em><strong>Funded PhD Studentship in Algebra.</strong></em> Please include the name of your preferred supervisor as listed.  Please state clearly in the Finance section that the funding source you are applying for is <em><strong>EPSRC Doctoral Landscape Award 2025/26: Pure Mathematics.</strong></em></p> <p>If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below).</p> <p><em>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></p> <p style="margin-bottom:11px">Applications will be considered after the closing date.  Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application.  We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</p> <p>Please note that you must provide the following documents in support of your application by the closing date of Friday 28 February 2025:</p> <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.

<p class="MsoNoSpacing">A highly competitive EPSRC Doctoral Landscape Award providing full academic fees, together with a tax-free maintenance grant at the standard UKRI rate (£19,237 in academic session 2024/25) for 3.5 years.  Training and support will also be provided.</p> <p>This opportunity is open to all applicants.  All candidates will be placed into the EPSRC Doctoral Landscape Award Competition and selection is based on academic merit.</p> <p><strong>Important:</strong> Please note that that the award does <em><strong>not</strong></em> cover the costs associated with moving to the UK.  All such costs (<a href="https://www.leeds.ac.uk/international-visas-immigration/doc/applying-student-visa">visa, Immigration Health Surcharge</a>, flights etc) would have to be met by yourself, or you will need to find an alternative funding source. </p> <p>Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.</p>

<p>For further information about your application, please contact PGR Admissions by email to <a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a></p> <p>Please contact individual supervisors listed for information about projects.</p>