Publications

Members:

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

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.

Professor Brita Nucinkis:

Dr Aditi Kar:
I am interested in Geometric Group Theory, which studies the structure of infinite groups via their actions on geometric spaces.

Publications

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.

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:
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

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.

Publications

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.

Professor Rainer Dietmann:

Dr Martin Widmer:
Height bounds, arithmetic statistics, Northcott property, Bogomolov property, class number problems, and Diophantine approximation.
Current PhD students: Reynold Fregoli

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.

Publications

Members:

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

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 Koenraad Audenaert:
Quantum information theory, Matrix analysis (with a focus on matrix inequalities).

Professor Francisca Mota-Furtado:

Professor Rüdiger Schack:
Quantum information theory, quantum cryptography and quantum Bayesianism. 

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.

Publications

Members:

Dr Alexey Koloydenko

Dr Teo Sharia

Dr Vadim Shcherbakov:
My general research interests are in applied probability. I am working on Markov processes with interaction (multivariate birth-and-death processes, competition processes, growth processes on graphs etc) and on applications of probability to finance.