Algebra and Number Theory

The research activities of the Algebra and Number Theory group at Durham fall into the following broad categories:

• Representation theory (of finite groups of Lie type, algebraic groups, and p-adic groups) sheds important light on properties of groups, the central algebraic building blocks. Key themes include generalizations of Deligne–Lusztig theory to reductive groups over finite rings, supercuspidal representations, and the geometry of Langlands parameters. Staff members: Shotton, Stasinski, Girsch
• Arithmetic geometry (automorphic forms, L-functions, polylogarithms) provides powerful tools for exploring number-theoretic questions, including p-adic interpolation of special values of L-functions, theta lifts and geometric cycles on arithmetic manifolds, and the connections between multiple polylogarithms and algebraic K-theory. Staff members: Abrashkin, Bouganis, Funke, Gangl
• Tropical algebraic geometry studies algebraic varieties through a piecewise-linear combinatorial lens. Research has a strong computational flavour, encompassing algorithms for tropical varieties and Grassmannians and applications to enumerative geometry and moduli spaces. Staff members: Ren, Schleis
• Analytic number theory uses tools from real, complex and harmonic analysis to study the properties of arithmetically interesting sequences like the prime numbers. Important themes in this subject include: the study of exponential and character sums; the behaviour and distribution of multiplicative functions; analytic aspects of automorphic forms; and the role of number theory in ergodic theory and additive combinatorics. Staff members: Mangerel

Academic Staff