# 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 David Bate
**Geometric measure theory, real analysis.

**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 Siri Chongchitnan**

Cosmology, theoretical astrophysics, mathematics education.

**Dr Sam Chow**

Diophantine equations, diophantine approximation, analytic number theory, additive combinatorics.

**Dr Radu Cimpeanu**

Applied mathematics, mathematical modelling, scientific computing, asymptotic analysis, computational fluid dynamics, interfacial flows, wave propagation, industrial mathematics.

**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 Emanuele Dotto**

Algebraic topology, homotopy theory, algebraic K-theory, equivariant homotopy theory.

**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.

**Dr Thomas Hudson**

Micromechanics of materials: Crystalline defects, especially dislocations and their evolution; Thermodynamic limits: linking microscopic and macroscopic properties of solids; Metastability and temperature-driven evolution of defects. Asymptotic methods in the Calculus of Variations, PDE and Stochastic Analysis (Gamma-convergence techniques, Stochastic Homogenization, Large Deviations Theory). Coarse-graining for dynamical systems (The Mori-Zwanzig formalism).

**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 Hong Liu**

Extremal and probabilistic combinatorics, graph theory, Ramsey theory and combinatorial number theory.

**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 Shreyas Mandre**

Partial differential equations, fluid and solid mechanics, asymptotic and perturbation methods, computational methods, engineering science.

**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 Joel Moreira**

Dynamical systems, ergodic theory and applications to arithmetic Ramsey theory, combinatorics and number theory.

**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 Felix Schulze**

Geometric analysis, partial differential equations and differential 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.

Uncertainty quantification, inverse problems, probabilistic numerics, data science.

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

**Dr Florian Theil**

Partial differential equations, discrete systems.

**Dr Adam Thomas**

Algebraic groups, finite groups of Lie type, Lie algebras, representation theory.

**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.

**Professor Nikolaos Zygouras**

Probability (including integrable probability, random media, SPDEs, statistical mechanics). I am also interested in the interactions of probability with integrable systems, representation theory and combinatorics.