# Permanent Staff and their Research Interests

**Dr Stefan Adams**

Large deviation theory, probability theory, Brownian motions, statistical mechanics, gradient models, multiscale systems

**Dr Claude Baesens**

Dynamical systems and applications to physics; exponential asymptotics

**Professor Keith Ball
**Functional Analysis, High-dimensional and Discrete Geometry, Information Theory

**Professor Dwight Barkley**

Applied and computational mathematics - nonlinear phenomena

**Dr Hugo van den Berg**

Mathematical biology

**Dr Christian Boehning
**Algebraic geometry, representation and invariant theory, derived category methods in birational geometry, birational automorphism groups, unramified cohomology and applications of K-theory in birational geometry

**Professor Brian Bowditch**

Hyperbolic geometry, low-dimensional topology, geometric group theory

**Dr Ed Brambley****
**Aeroacoustics (mathematical modelling and computational theory); mathematical modelling of industrial metal forming; fluid dynamics; applied mathematics

**Professor Gavin Brown
**Algebraic geometry, especially classification, birational geometry and constructions of varieties (both using computational algebra and not)

**Professor Nigel Burroughs**

Mathematics applied to cell biology, (biophysical) models of dynamic spatial biological systems, analysis of experimental data using Bayesian model fitting methods (Markov chain Monte Carlo algorithms)

**Dr Inna (Korchagina) ****Capdeboscq**

Group theory, groups of Lie type, finite simple groups

**Dr Colm Connaughton**

Non-equilibrium statistical mechanics, fluid dynamics and turbulence, nonlinear waves, interacting particle systems

**Professor John Cremona**

Number theory: elliptic curves, modular forms, computational number theory

**Dr Andreas Dedner
**Numerical analysis and scientific computing, Higher order methods for solving non-linear evolution equations, Generic software design for grid based numerical schemes, Geophysical flows, Radiation magnetohydrodynamics

**Dr Louise Dyson
**Mathematical modelling of biological systems, especially the epidemiology of neglected tropical diseases and the analysis of biological systems in which noise plays an important role

**Professor Charles Elliott**

Partial differential equations and their applications: Analysis, Geometric PDEs, Free Boundaries and Interfaces, Biology, Social-sciences, Materials, Finite Elements, Numerical Analysis, Computations

**Dr Adam Epstein**

Complex analytic dynamics; Riemann surfaces; value-distribution theory

**Professor Vassili Gelfreich**

Analysis and dynamical systems

**Dr Agelos Georgakopoulos**

Infinite graphs, and their interactions with other fields of mathematics

**Dr Tobias Grafke**

Rare events, fluid dynamics and turbulence, large deviation theory, metastability, non-equilibrium statistical mechanics, active matter.

**Professor John Greenlees**

Algebraic topology, homotopy theory, equivariant cohomology theories, derived categories and commutative algebra.

**Dr Stefan Grosskinsky**

Applied probability, stochastic processes and complex systems, statistical mechanics, large-scale dynamics of stochastic particle systems

**Dr Adam Harper****
**Analytic number theory, and connections with probability and combinatorics

**Professor Derek Holt**

Group theory, computational algebra

**Professor Matthew Keeling**

Mathematical modelling of population dynamics, especially infectious diseases and evolution. I am interested in how heterogeneities impact on population dynamics, in particular spatial structure, social networks and stochasticity. I study the following diseases: foot-and-mouth disease, bovine TB, influenza, measles, bubonic plague

**Professor Robert Kerr**

Partial Differential Equations, Computational Fluid Dynamics, Geophysical Fluid Dynamics

**Dr Markus Kirkilionis**

Mathematical biology, dynamic network models, complex systems, numerical analysis, pattern formation, physiologically structured Population models, (monotone) dynamical systems

**Professor Roman Kotecky**

Probability; statistical physics; theory of phase transitions

**Dr Oleg Kozlovski**

Dynamical systems, ergodic theory, mathematical physics, financial mathematics

**Professor Daniel Kral
**Extremal combinatorics, structural and algorithmic graph theory, and combinatorial limits

**Dr Daan Krammer**

Algebra, Braid Groups, Knots

**Dr David Loeffler
**Modular and automorphic forms, Iwasawa theory, and p-adic analysis

**Dr Martin Lotz
**Numerical optimization, computational complexity, probabilistic analysis of algorithms, computational geometry and topology, geometric probability and applications to dimension reduction

**Professor Vadim Lozin**

Graph theory, combinatorics, discrete mathematics

**Professor Robert MacKay FRS**

Dynamical systems theory and applications, complexity science

**Dr Diane Maclagan**

Combinatorial and computational commutative algebra and algebraic geometry

**Dr Andras Mathe
**Geometric measure theory, fractal geometry

**Professor Ian Melbourne
**Ergodic theory and dynamical systems; links with stochastic analysis

**Dr Mario Micallef**

Partial differential equations; differential geometry

**Professor David Mond**

Singularity theory, algebraic geometry

**Dr Andrea Mondino
**Geometric analysis, differential geometry, optimal transport, partial differential equations

**Professor Christoph Ortner****
**Numerical analysis, scientific computing, multi-scale methods, molecular simulation, atomistic materials modelling

**Professor Oleg Pikhurko**

Extremal combinatorics and graph theory; random structures; algebraic, analytic and probabilistic methods in discrete mathematics.

**Professor Mark Pollicott**

Thermodynamic Formalism, with applications to geometry, analysis and number theory

**Professor David Rand**

Mathematical biology, pure and applied dynamical systems

**Professor Miles Reid FRS**

Algebra and geometry, algebraic geometry, classification of varieties, minimal models of 3-folds and higher dimensional algebraic varieties, singularities of 3-folds and higher dimensional algebraic varieties, orbifolds and their resolution, McKay correspondence

**Dr Magnus Richardson
**Theoretical neuroscience, quantitative physiology, stochastics, statistics, machine learning

**Dr Filip Rindler
**PDEs, calculus of variations, geometric measure theory

**Professor James Robinson**

Partial differential equations in fluid dynamics; embedding properties of finite-dimensional sets; infinite-dimensional dynamical systems

**Dr Kat Rock**

Dynamic, mechanistic models of vector-borne diseases. ODE, PDE and stochastic model approaches to directly address applied research or policy questions

**Professor Jose Rodrigo**

Analysis, partial differential equations and theoretical fluid mechanics

**Dr Dmitriy Rumynin**

Representation theory

**Dr Saul Schleimer**

Geometric topology, group theory, and computation

**Dr Marco Schlichting
**Algebraic K-theory and higher Grothendieck-Witt groups of schemes; A^1-Homotopy Theory and Motivic Cohomology; Derived Categories, algebraic topology and algebraic geometry

**Professor Richard Sharp
**Ergodic theory, dynamical systems, applications to geometry, combinatorial and geometric group theory, quantum chaos and noncommutative geometry

**Professor Samir Siksek**

Arithmetic Geometry, Rational Points, Modular Curves

**Professor John Smillie**

Translation surfaces and complex dynamics in higher dimensions

**Dr Vedran Sohinger**

Nonlinear Dispersive PDEs, Harmonic Analysis, and Quantum many-body problems

**Professor Colin Sparrow**

Dynamical systems, differential equations, bifurcations, game theory, discrete event systems

**Dr James Sprittles
**Applied mathematics, computational fluid dynamics, interfacial flows, porous media, rarefied gas flow

**Dr Björn Stinner
**Modelling of free boundary problems, analysis of nonlinear PDEs, finite element methods

**Dr Damiano Testa
**Algebraic geometry, number theory

**Dr Florian Theil**

Partial differential equations, discrete systems

**Dr Michael Tildesley
**Mathematical Modelling of Infectious Diseases. Modelling of control policies in the presence of partial information. I work on a range of diseases such as avian influenza, foot-and-mouth disease, rabies and bovine tuberculosis

**Professor Peter Topping**

Geometric Analysis, Nonlinear PDE, Differential Geometry

**Dr. Roger Tribe**

Probability, in particular interacting particle systems and stochastic partial differential equations

**Dr Daniel Ueltschi**

Statistical mechanics, probability theory

**Professor Karen Vogtmann**

Geometric group theory, low-dimensional topology, cohomology of groups

**Dr Sebastian Vollmer
**Monte Carlo Methods, Stochastic Gradient Methods, Stochastic Processes

**Dr Marie-Therese Wolfram
**Partial differential equations, mathematical modeling in socio-economic applications and the life sciences, numerical analysis

**Dr David Wood**

Dynamical systems, bifurcations with symmetry, applications to biology and industry

**Professor Oleg Zaboronski**

Non-equilibrium statistical mechanics of interacting particle systems, random matrices and integrable systems

**Dr Weiyi Zhang**

Symplectic topology, complex geometry and their interactions