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.

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:

• Quivers and their representations; Moduli spaces in representation theory and mathematical physics; Cherednik algebras and double affine Hecke algebras.
• Algebraic structures connected with combinatorial solutions of the Yang-Baxter equation and Pentagon equation.
• Algebras and computation for statistical mechanics; combinatorial and geometric algebra in the interface of mathematics with physics.
• (Extended) topological quantum field theories; Hopf algebras and low dimensional topology; Algebraic models for homotopy types.
• Representations, invariants and actions of reductive algebraic groups in characteristic p.
• Spectral sequences on nilpotent Lie groups, homotopy transfer theorem on homogeneous Lie groups, Lie algebra cohomology of nilpotent Lie groups.
• Differential Galois theory; Difference algebraic groups.

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.

Please visit our website find out more about these research areas and eligible academic supervisors including how to contact them directly.