Pure Mathematics
University of Birmingham
Microlocal analysis explores the classical/quantum correspondence in partial differential equations (PDEs). For example, the concept of symbol quantisation in the theory of pseudodifferential operators links classical observables (functions on phase space) with quantum operators.
- Location
- Birmingham, United Kingdom
- Deadline
- 22 October 2026
- Funding
- Funded PhD Project (UK Students Only)
Pure Mathematics
University of East Anglia
About the Project Primary Supervisor: Dr Jonathan Kirby Model theory is traditionally done with “classical first-order logic”, the logic which allows unlimited use of the operators AND, OR, NOT, with the EXISTS and FOR ALL quantifiers. More recently, positive logic has emerged as a useful generalisation.
- Location
- Norwich, United Kingdom, United Kingdom
- Deadline
- 30 November 2026
- Funding
- Self-Funded PhD Students Only
Pure Mathematics
University of East Anglia
About the Project Primary Supervisor: Prof Vanessa Miemietz Categorification has led to major advances in representation theory in the last 30 years, including the proof of Broué’s abelian defect group conjecture for symmteric groups and the proof of the Kazhdan—Lusztig conjectures for all Coxeter types. Classically, a representation of an algebra (a ring that is also a vector space) is an action of the latter on a vector space via linear maps.
- Location
- Norwich, United Kingdom, United Kingdom
- Deadline
- 30 November 2026
- Funding
- Self-Funded PhD Students Only
Pure Mathematics
University of Birmingham
About the Project Projects available in a range of topics in representation theory and Lie theory. These are centred around questions in the representation theory of Lie algebras and algebraic groups and are likely to involve a blend of algebraic, combinatorial and geometric methods.
- Location
- Birmingham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (UK Students Only)
Pure Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying. Graphs are among the most basic combinatorial objects studied in mathematics, consisting simply of a collection of objects and connections among them.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Dr Richard Hepworth-Young Dr M Grant
Pure Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying. This PhD project is at the intersection of complex analysis, partial differential equations, and geometric analysis.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Pure Mathematics
University of Birmingham
About the Project The algebraic properties of groups are intricately linked with the geometric properties of the spaces they act on. For infinite groups, there are typically many choices of "natural" actions on geometric spaces. While these spaces may be locally very different, they have the same coarse (large-scale) structure.
- Location
- Birmingham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (UK Students Only)
Pure Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying. Coarse geometry is the study of asymptotic properties of metric spaces.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Pure Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying. Following Gromov, this project is concerned with coarse geometry of metric spaces.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Pure Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying. The representation theory of many families of finite groups can be presented in terms of combinatorial objects.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Pure Mathematics
University of Birmingham
About the Project Extremal graph theory is one of the most active and dynamic branches of combinatorics. The fundamental goal of the area is to understand what conditions force a graph to contain some substructure. For example, Mantel’s theorem – proved more than a century ago – determines how many edges a graph on n vertices needs to guarantee it contains a triangle.
- Location
- Birmingham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (UK Students Only)
Pure Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Pure Mathematics
University of Birmingham
About the Project The probabilistic method is a powerful tool which has been especially influential in the fields of combinatorics and computer science. In the context of combinatorics, this method was pioneered by Erdős, who demonstrated that random constructions could often be effective in settings where explicit constructions are infeasible.
- Location
- Birmingham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Pure Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying. Lie algebras originally appeared in the work of the Norwegian mathematician Sophus Lie as infinitesimal symmetries of geometric objects called nowadays manifolds.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Pure Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying. The theory of p-local groups developed by C. Broto, R. Levi and B.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Pure Mathematics
University of Birmingham
About the Project The main objectives in this project are tomographic operators such as X-ray transform and Radon transform. By investigating the Lp-boundedness properties, we will study the smoothing properties of these operators.
- Location
- Birmingham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only