Professor Rainer Dietmann:

I work at the interface of Analytic Number Theory and Diophantine equations. My current research interests include probabilistic
Galois theory, applications of the circle method to systems of Diophantine equations, including investigating their solubility over
local fields, lines on rational hypersurfaces, gaps between arithmetically defined sequences and additive combinatorics.

Professor James McKee:

My research interests lie at the interface of number theory and combinatorics, with computational leanings. My recent work has mostly been connected with Pisot numbers, Salem numbers, other algebraic numbers whose Galois conjugates are geometrically constrained, and associating algebraic numbers to certain combinatorial objects.

Dr Eira Scourfield (Emeritus):

Arithmetic functions such as Euler’s function and the sum-of-divisors function have been studied for centuries. My current research aims to derive asymptotics for the number of divisors and exact divisors up to y of these functions at primes up to x with y large in terms of x.

Professor Martin Widmer:

I work on the theory of height functions, on problems related or motivated by Lehmer’s conjecture. For instance, I am trying to understand which fields of algebraic numbers have infinitely many elements of bounded arithmetic complexity (Weil height), and the implications to other subjects such as logic (decidability), Diophantine geometry, and “exotic” Diophantine approximation. I am also interested in counting various algebraically defined objects of arithmetic interest, and, more generally, to study their distribution (arithmetic statistics). Currently, I am focussing on problems related to the distribution of  class groups of number fields. 

More details about my research can be found on my personal webpage.