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Department of Mathematical Sciences

Pure Mathematics

Research

We are a very active and successful research group in several exciting areas of pure mathematics. The department members have well respected international reputations.

We work in the following broad fields of mathematics:

In the last few years several algebraists have been appointed as new members of staff. We are able to offer a very broad spectrum of topics within the general area of algebra, including

  • Galois groups of local fields and ramification theory
  • group schemes and p-adic representations
  • automorphic forms, representation theory
  • cohomology of arithmetic groups
  • algebraic cycles & algebraic K-theory
  • polylogarithms, periods and relations to Feynman integrals
  • Diophantine approximation.
In the last few years several geometers have been appointed as new members of staff. Our research covers a very broad spectrum of topics within the general area of geometry:
  • complex geometry
  • cluster algebras
  • discrete groups
  • dynamical systems
  • hyperbolic geometry
  • Laplace and Schrödinger operators
  • locally symmetric spaces

Generally speaking, we are interested in the interplay between geometry and other areas of pure mathematics like algebra, combinatorics, dynamics, number theory, real and complex analysis.

Topology in Durham is represented by several members of staff who cover a wide range of research topics in algebraic and geometric topology. These include

  • braids
  • configuration spaces
  • knot theory
  • Morse theory
  • persistent homology
  • 3- and 4-dimensional manifolds
  • topology of closed 1-forms

Postgraduate Study

We are a very active and successful research group offering postgraduate training in several exciting areas of pure mathematics. The department members have well respected international reputations and great experience in supervising students.


We offer a taught MSc and an extensive PhD programme. The Willmore Pure Mathematics Postgraduate Award is open to outstanding candidates starting their PhD studies here.

The department runs a variety of research seminars and colloquia, some of them are specially designed for postgraduate students. There are regular joint meetings between postgraduate students from our department and from the University of Newcastle. Postgraduate students in Durham profit from the rich scientific environment and stimulating contacts with our colleagues from the other research groups of the department (mathematical physics, statistics and probability, numerical analysis). In addition, Durham is the permanent home of the famous London Mathematical Society Symposia, and these prestigious international events bring distinguished mathematicians to Durham from all over the world.



Group Members