The Department of Mathematics pursues research in a wide range of topics in pure, applied and applicable mathematics, including algebra, discrete mathematics, number theory, quantum dynamics, information security and probability and statistics.
We have regular seminars covering the range of our research interests.
Archive of old Pure Mathematics Seminars (up to May 2018)
We run an active PhD research programme covering an array of topics. All of our academic staff are happy to take on new PhD students.
To check out the list of our publications: click here
To read about our projects: click here
Our research groups and their members:
Algebra
To check out the list of our publications: click here
Our members:
Dr Yiftach Barnea:
My general research area is Algebra. In particular I wrote papers in the following areas:
- Group Theory: Asymptotic Group Theory, Pro-p Groups, Profinite Groups, Totally Disconnected Locally Compact Groups, Algebraic Groups over Local Fields.
- Lie Algebras: Finite Dimensional Lie Algebras, Graded Lie Algebras.
Dr Aditi Kar:
I am interested in Geometric Group Theory, which studies the structure of infinite groups via their actions on geometric spaces.
Professor Brita Nucinkis:
My research is in cohomological and geometric properties of groups, using methods from homological algebra, algebraic topology and geometric group theory. Currently, I am interested in finiteness conditions for classifying spaces, and in studying cohomological and metric properties of groups related to Thompson’s group F.
Current PhD students: Victor Moreno, Alexandra Embleton, Nick Winstone
Professor Mark Wildon:
My main research interest is the representation theory of symmetric group and related algebras. This subject sees an attractive interplay of ideas from algebra and combinatorics, and has many easily stated but deep open problems. I have also published papers on searching games, Brownian motion, and enumerative combinatorics (counting things!).
Current PhD students: Jasdeep Kochhar, Eoghan McDowell
Discrete Mathematics and its Applications
To check out the list of our publications: click here
Our members:
Professor Simon Blackburn:
My research interests are in combinatorics and its applications, especially to cryptography and communication theory, and in group theory.
Current PhD students: Luke Stewart, Liam Medley.
Professor Stefanie Gerke:
My main interests are in the area of graph theory in general, and in random graph theory and algorithms in particular.
Current PhD students: Balazs Mezei, Jiangdong Ai
Professor Iain Moffatt:
I work in algebraic combinatorics, matroid theory, topological graph theory, and knot theory. My research centres on the interface of combinatorics and topology. I am particularly interested in the ways in which combinatorial and topological structures can be encoded in one another, and in exploiting such connections to solve hard problems in combinatorics and topology.
Dr Siaw-Lynn Ng:
My main research is in the fields of finite geometry, combinatorics and security protocols. My research focuses on the interaction between discrete mathematics and information security. Recent research areas are combinatorial problems in cryptography and communications, and the balancing of privacy and accountability in anonymous networks.
Current PhD students: Chatdanai Dorkson
Dr Martin Widmer:
Number theory: Height bounds, arithmetic statistics, Northcott property, Bogomolov property, class number problems, and Diophantine approximation.
Discrete geometry: geometry of numbers, lattices, convex geometry.
Logic: model theory and applications in number theory (o-minimality, in particular), decidability and connections to number theory.
Current PhD students: Reynold Fregoli
Number Theory
To check out the list of our publications: click here
Our members:
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:
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.
Dr Martin Widmer:
Number theory: Height bounds, arithmetic statistics, Northcott property, Bogomolov property, class number problems, and Diophantine approximation.
Discrete geometry: geometry of numbers, lattices, convex geometry.
Logic: model theory and applications in number theory (o-minimality, in particular), decidability and connections to number theory.
Current PhD students: Reynold Fregoli
Quantum Dynamics
To check out the list of our publications: click here
Our members:
Professor Koenraad Audenaert:
Quantum information theory, Matrix analysis (with a focus on matrix inequalities).
Professor Jens Bolte:
My research area is Mathematical Physics. I am in particularly interested in quantum graphs and in semiclassical analysis. In the former area one studies properties of one dimensional quantum systems with a complicated topology. In the latter area approximations of quantum systems in terms of classical quantities are investigated.
Professor Emeritus John Essam:
My research is in the general area of phase transitions. Examples are ordering of interacting spin (Potts) models, polymer collapse and percolation through random networks. All involve the enumeration of graphs embedded in crystal lattices. A model, related to traffic flow, of particles hopping along a chain can be formulated as a polymer collapse model.
Dr Alastair Kay:
I am interested in quantum computation and quantum information, specifically focussed on theoretical ideas to help reduce the technical demands on future experimental realisations of quantum computers and quantum technologies. We are anticipated to be on the cusp of a new, quantum, technological revolution, with these devices at its forefront.
Current PhD students: Catherine Keele
Professor Francisca Mota-Furtado:
I work on time-dependent quantum systems and, in particular, the interaction of atoms with intense short pulse electromagnetic radiation. The non-linear interaction of a laser field with the atom results in multiple new effects such as high harmonic generation and re-scattering of the ionised electron. These are studied using both classical and quantum approaches.
Professor Pat O'Mahony:
My current research is aimed at understanding the dynamics of the interaction of short intense laser pulses with atoms. I use classical, semi-classical and quantum theories (the time dependent Schrödinger equation) to study the problem. Attosecond pulses (extremely short pulses of a duration on the order of 10-18 seconds) make it possible to study electron motion in atoms in real time.
Current PhD students: Sam Jenkins
Professor Rüdiger Schack:
Quantum information theory, quantum cryptography and quantum Bayesianism.
Statistics and Probability
To check out the list of our publications: click here
Our members:
Dr Alexey Koloydenko:
I work on computationally intensive applications of Probability and Statistics, including non-Euclidean statistics, diffusion tensor MRI, biomedical imaging based on Raman spectroscopy and fluorescence to automate diagnosis of skin and breast cancers. I also work on hidden Markov models, including Bayesian ones, and algebraic methods in probability and statistics.
Dr Teo Sharia:
My research interests are: stochastic approximation, parametric estimation theory, statistics of stochastic processes, recursive estimation procedures, time series analysis, hidden Markov models.
Dr Vadim Shcherbakov:
My general research interests are in applied probability.
