Algebra and representation theory of:

– quantum groups

– Kac-Moody algebras

– double affine Hecke algebras

– quantum sy...

# Academic Staff

Martina Balagovic, Magnus Bordewich, David Bourne, Camila Caiado, Stefan Dantchev, Michael Dritschel, Andrew Duncan, Anna Felikson, John Fitzgerald, Leo Freitas, Tom Friedetzky, Max Gadouleau, Herbert Gangl, Ostap Hryniv, John Hunton, Ioannis Ivrissimtzis, Ian Jermyn, Matthew Johnson, Peter Jorgensen, Evgenios Kakariadis, Victor Khomenko, David Kimsey, Stefan Kolb, Maciej Koutny, Andrei Krokhin, Andrew Lobb, Barnaby Martin, George Mertzios, Tom Nye, Boguslaw Obara, John R Parker, Daniel Paulusma, Norbert Peyerimhoff, Marta Pietkiewicz-Koutny, Bernard Piette, Sarah Rees, Dirk Schütz, Jason Steggles, David Stewart, Iain Stewart, Pavel Tumarkin, Alina Vdovina, Andrew Wade

Algorithms for the reconstruction of phylogenetic (evolutionary) trees and networks. The mixing time of Markov chain Monte Carlo algorithms for statistical physics mod...

David Bourne works on pattern formation problems in material science. He is particularly interested in crystallization problems: proving that particle systems have per...

Bayesian approaches to modelling and uncertainty quantification for large complex systems.

Applications include: population dynamics including agent-based model...

Computational Complexity, Propositional Proof Complexity, Satisfiability Solving, Algorithms in Topology

Michael Dritschel works in

– operator theory

– operator algebras

– function theory

Discrete aspects include function algebras...

Geometric group theory:

– Hyperbolic groups

– partially commutative (right angled) Artin groups

– pregroups, graphs of groups and t...

Cluster algebras, Coxeter groups, hyperbolic geometry, discrete group actions and interaction of all the things above.

John Fitzgerald works on model-based methods of systems engineering, leveraging the mathematical semantics of design languages to permit computer-assisted exploration ...

Formal modelling and proof of systems and software. Current focus is on the safety/dependability of medical devices and security protocols behaviour (e.g. EMV payments...

Randomised algorithms, discrete probability; combinatorics; efficient primitive operations inspired by problems in parallel/distributed systems (communication: broadca...

Max Gadouleau’s research interests were at first based on coding theory, network coding and information theory. He has worked on their application to cryptograph...

Ideal tessellations of hyperbolic 3-space arising from discrete groups produce interesting elements in algebraic K-groups of number rings; moreover, they create beauti...

– discrete state Markov chains (both finite and infinite) and their applications (eg., to biology),

– random walks,

– properties of hitti...

Aperiodic structures, tilings, topology, esp. algebraic topology, symbolic dynamics, topological dynamics,

homological and homotopical methods, topological group...

Ioannis Ivrissimtzis is interested in the applications of triangle meshes in design, visualisation and

simulation. He works in the area of mesh subdivision, whic...

Statistical modelling of shape and geometry, applied to computer vision and graphics. Problems include: relations amongst continuum models and discrete formulations as...

Algorithms and complexity of problems on graphs. Structure of solution graphs of problems. Characterizing classes of tractable problem instances.

Peter Jorgensen’s research in homological algebra gives rise to many discrete and combinatorial structures: surface triangulations, polygon dissections, and frie...

A main trend in Operator Algebras is to examine operators related to geometric structures. Depending on the choice of the quantization one may ask how this encodes the...

Application of formal methods to verification and synthesis of concurrent systems. Model checking of Petri nets and synthesis of asynchronous circuits.

Spectral Theory

Representation Theory: Kac-Moody algebras; quantum groups, quantum symmetric pairs; relations to braid groups, harmonic analysis, homological algebra, integrable syste...

Maciej Koutny’s research interests centre on the theory of distributed and concurrent systems, including both theoretical aspects of their semantics and applicat...

Andrei Krokhin’s research is about mathematical and algorithmic aspects of Constraint Satisfaction Problems (CPSs). Constraints are usually specific by relations...

Andrew Lobb studies three- and four-dimensional spaces – the dimension is high enough to be interesting but not so high that the interesting topology can be undo...

Computational and proof complexity, especially classifications and the boundary of tractability. Constraint satisfaction problems; logic in computer science; graph the...

George Mertzios’ research interests lie in the algorithmic aspects of basic combinatorial and graph problems which are also motivated by practical applications. ...

Main interest: evolutionary trees (phylogenies)

– space of trees has a CAT(0) geometry

– statistical analysis is via geometry in tree-space

Boguslaw Obara is an expert in image informatics approaches for processing and analysis of multidimensional images obtained by a wide spectrum of micro and macro imagi...

Discrete groups and hyperbolic geometry. In particular:

– fundamental polyhedra, tilings and crystal structures;

– spaces of discrete groups an...

– graph algorithms (in particular for graph colouring and variants / generalisations of graph colouring)

– structural graph theory (in particular, sp...

Spectral graph theory, Geometric group theory, discrete geometry, hyperbolic geometry, combinational and synthetic curvature notions, Cayley graphs, expanders, (higher...

Marta Pietkiewicz-Koutny’s research concentrates on Theory of Concurrency; models of concurrent systems, especially Petri nets; synthesis of concurrent systems f...

– Bio-Physics

– Polymer Network Dynamics

– Pre Darwinian Ancestors

– Polaron Dynamics on Lattices

– Geometry of P...

Geometrical, combinatorial and computational aspects of group theory, especially

– decision problems

– links between group theory and formal la...

Knot Theory, in particular Khavanov homology and stable homotopy, cohomology operations, applications to 3- and 4-dimensional topology. Configuration spaces of linkage...

Jason Steggles’ research focuses on formal techniques for modelling and reasoning about computing systems. This includes working on new theoretical modelling fra...

David Stewart works on various aspects of modular Lie theory, aprticularly the subgroup (scheme) structure of algebraic groups, and their representation theory.

Current interests lie in the mathematical and computational aspects of interconnection networks and their relationships with distributed-memory multi processes, networ...

Coxeter groups, hyperbolic geometry, fundamental domains, cluster algebras, quiver mutations, combinatorics of polytopes.

Geometric group theory, topological graph theory, Knot theory

Andrew Wade is a probabilist interested in stochastic processes and random discrete structures, particularly: random walks, interacting particle systems, and geometric...