Mathematics PhD: Categorification and the local Langlands correspondence

Mathematics PhD: Categorification and the local Langlands correspondence

Quick Decision

Strong but verify fit. This is a high-value pure-mathematics studentship for a candidate already comfortable with proof-heavy algebra, representation theory and number theory. The advertised work first makes a categorical representation of a quantum group precise for p-adic general linear groups, then may carry information through local Langlands and into derived categories. Co-supervision by Shaun Stevens and Vanessa Miemietz aligns closely with those two sides. The advert restricts funding to UK students but gives no award amount or coverage; contact both supervisors now about the award and exact thesis scope. The deadline is 30 November 2026, with a 1 February 2027 start.

Research Problem and Doctoral Work

The project sits between two active mathematical languages. Local Langlands connects representations of p-adic groups with arithmetic parameters; higher representation theory studies categorical actions, where algebraic operators are represented by functors and their relations. The advertised starting point is to make precise, for the p-adic case, a 2-representation of a quantum group analogous to a result for finite general linear groups. The next possible step is to transfer information through the local Langlands correspondence and perhaps extend the framework to relevant derived categories. The latter is explicitly a possible direction rather than a promised result.

The likely work is proof construction: specify categories and functors, establish the required relations, compare the p-adic construction with the finite-group precedent, and test what structure is preserved under the correspondence. The project description does not state a fixed theorem, expected papers, software requirement or experimental component. A useful early discussion is therefore about the first-year mathematical target and what counts as a viable narrower thesis if the derived extension proves too ambitious.

School, Programme and Field Context

The degree-awarding institution is the University of East Anglia (UEA), and the listed school is Engineering, Mathematics and Physics. REF 2021 assessed UEA Mathematical Sciences as 28% 4-star and 66% 3-star overall, with all eligible staff submitted. This is a peer-reviewed research profile, not a rank or a guarantee about a single group. The unit's environment statement reports 20 permanent academics, 36 PhD graduates since REF2014 and a research-income total of £4.2m; its algebra group explicitly connects representation theory, homological methods, category theory and number theory.

UEA's general postgraduate research guide describes a three-year PhD supported by primary and secondary supervisors in a research group. The vacancy itself gives two named co-supervisors, a specific advantage for an interdisciplinary pure-mathematics topic. Public materials do not establish a compulsory course sequence, a taught catch-up curriculum, exact annual milestones or whether the student joins a particular seminar cohort. Ask how the doctoral registration and training plan fit the 1 February start.

Supervisor and Lab Assessment

Stevens works on explicit representation theory of p-adic groups and local Langlands, leads the algebra/number-theory/logic/representations group and reports ten PhD completions. Miemietz works on representation theory and homological structures, is accepting students and invites funding discussions for projects outside currently advertised areas. Their expertise matches the project unusually well. The group lists an active EPSRC-supported 2-representation project for 2025–2028, which confirms current activity but does not show that this studentship shares that grant.

Recent work helps judge the intellectual environment. Miemietz and coauthors' 2025 paper develops pretriangulated 2-representations using dg-algebra morphisms, a useful adjacent precedent for the advertised possible derived-category direction. A 2026 paper starts a categorification of induction for extended affine type A Soergel bimodules; her 2024 paper applies projective-functor methods to a wider class of holonomic modules. Stevens's recent output concerns local parameters, converse theorems and reducibility for p-adic groups. These papers show active nearby research, not a guarantee that the thesis will reproduce any one result.

Funding, Application, and Living Cost

The listing calls this a studentship and says funding is for UK students; its amount is “not specified.” That supports treating it as an advertised restricted studentship, not as evidence that the place is self-funded. It does not establish stipend, duration, fee payment, research allowance or exact UK eligibility. Do not assume the award is UKRI-funded. As a comparator only, UKRI's 2026/27 minimum full-time stipend is £21,805, and its home-fee contribution is £5,238; UKRI warns that international students may owe a fee gap. UEA's 2026/27 table lists £21,650 for first-year overseas Mathematics research study. Confirm the actual fee code and award letter.

UEA's 2026/27 accommodation list gives current campus 41-week en-suite prices of about £7,318–£8,590, an undergraduate-length benchmark rather than a doctoral housing quote. Actual Norwich rent, bills and the length of accommodation needed will vary. The visa maintenance threshold is not a realistic full-year budget and can change before the February 2027 start. With only about two months between the deadline and start, ask about funding, visa documents and enrolment timing before applying.

Applicant Fit and Preparation

Advertised minimum: a 2:1 bachelor's degree in mathematics. The project does not list coding, lab work or a specific master's degree as a formal requirement. Suggested preparation: strong proof-writing and prior study in abstract algebra, representation theory, category theory or number theory. These are fit signals inferred from the research, not extra admissions rules. Prepare a short account of a proof-based project, the mathematical questions you want to pursue, and any exposure to p-adic groups or categorical methods. Ask what knowledge can be learned during the doctorate and what is expected on day one.

Next Actions and Questions to Verify

Before applying: use the official project or staff pages to confirm a current contact route, then share a concise CV and a short note on mathematical preparation. Confirm the exact UK-student eligibility test, award amount and length, stipend, home-fee coverage, whether any overseas route exists, application portal and required documents. Ask what problem can realistically be scoped for the first year and whether formal courses or reading groups support the transition.

At interview: ask how responsibilities divide between the two supervisors, the cadence of meetings, the first-year proof milestones, and how the project will be narrowed if the derived extension is not feasible.

Before accepting: obtain written confirmation of the fee code, stipend, award term, research/travel support, registration date and any funding gap. No public evidence found makes the project low value; its niche is the source of its intellectual specificity.

Evidence and Sources

Project and research environment

• Algebra and representation research group
• School research environment
• REF 2021: Mathematics assessment profile
• REF 2021 mathematics environment statement
• Prior funded research in the area

Supervision and publications

• Shaun Stevens: research profile
• Vanessa Miemietz: research profile
• Miemietz et al. (2026), categorification paper
• Laugwitz and Miemietz (2025), derived 2-representations
• Mackaay et al. (2024), projective functor methods
• Stevens et al. (2026), local representation theory
• Adrian and Stevens (2025), local converse theorems
• Stevens et al. (2024), Langlands parameters

Training, funding and living costs

• UEA postgraduate research training guide
• 2026/27 overseas mathematics research fee
• UKRI 2026/27 stipend and fee rules
• UKRI studentship guidance
• UEA 2026/27 accommodation benchmark
• UK Student visa funds

Field and career context

• UK graduate and PhD outcomes data
• Mathematics research careers