Number Theory

Number Theory is one of the oldest disciplines of mathematics, and has connections to almost all other areas of pure mathematics. In Glasgow, we cover a broad spectrum of number theory and of its connections to other disciplines: we study, among many other topics,

• rational points on curves, surfaces, and higher dimensional varieties, utilising geometric, analytic, algebraic, and probabilistic techniques;
• classical objects of interest in algebraic number theory such as class groups, elliptic curves, higher dimensional abelian varieties;
• analytic number theory topics, such as the Riemann zeta and Dirichlet L-functions, the distribution of prime numbers, the circle method, and the Selberg and Brun sieves;
• diverse topics at the interface of number theory and representation theory, including (integral) Galois module structure, Galois representations, and automorphic forms, with numerous connections to representation theory of finite and of linear groups, p-adic Hodge theory, Lie theory, combinatorics, and other areas.

For more information, feel free to browse our members' web pages. More information about our group, our members, our activities, and a full list of our expertise, can be found at our Core Structures webpage.

Our group has an active PhD student community, and every year we admit new PhD students.  We welcome applications from across the world, and we encourage you to browse our available supervisors, and also to consult our general advice on how to navigate the application process.