# Research at Warwick

**This page lists permanent Warwick staff and Zeeman Lecturers, by roughly indicative research areas. Many staff are listed under more than one heading.**

**The department also hosts, or plays a significant part in, a number of research centres, which are listed at the bottom of the page.**

Christian Boehning, Inna Capdeboscq, John Greenlees (derived commutative algebra and representation theory), Derek Holt, Nicholas Jackson (category theory, homological algebra), Miles Reid (commutative algebra, Gorenstein rings, representation theory, McKay correspondence), Dmitriy Rumynin (representation theory, Lie algebras, Kac-Moody groups), Minhyong Kim (cohomology of profinite groups), Marco Schlichting (projective modules, quadratic forms, homology of groups), Adam Thomas (algebraic groups, Lie algebras, finite groups of Lie type, representation theory), Karen Vogtmann (cohomology of groups)

Christian Boehning, Gavin Brown (birational geometry; computational algebra), Minhyong Kim (arithmetical algebraic geometry), Chunyi Li (derived categories, moduli spaces), Diane Maclagan, David Mond, Miles Reid (classification of varieties; surfaces and 3-folds; orbifold geometry; graded rings; singularity theory), Dmitriy Rumynin (D-modules, homogeneous spaces, derived categories), Marco Schlichting (algebraic K-theory, derived categories, motives), Damiano Testa (curves, surfaces), Weiyi Zhang (almost complex geometry and symplectic topology)

Keith Ball, David Bate (geometric measure theory), David Elworthy (geometric stochastic analysis), András Máthé (geometric measure theory, fractal geometry, discrete analysis), Mark Pollicott (fractal geometry), Filip Rindler (geometric measure theory), José Rodrigo (singular integral operators, commutator estimates), James Robinson (dimension & embedding theory), Felix Schulze (geometric analysis), Vedran Sohinger (nonlinear dispersive PDEs), Peter Topping (geometric analysis)

Keith Ball, Sam Chow (arithmetic combinatorics), Agelos Georgakopoulos (infinite & finite graph theory), Adam Harper (additive combinatorics), Dan Kral, Hong Liu (extremal and probabilistic combinatorics, Ramsey theory), Vadim Lozin, Joel Moreira (arithmetic combinatorics), Oleg Pikhurko (extremal & probabilistic combinatorics; limits of discrete structures)

see also the Centre for Discrete Mathematics and its Applications (DIMAP)

**COMPUTATIONAL APPLIED MATHEMATICS**

Dwight Barkley, Radu Cimpeanu (fluid mechanics - interfacial phenomena, acoustics, scientific computing), Colm Connaughton (fluid dynamics, turbulence), Andreas Dedner (scientific computing, software framework design), Tobias Grafke (fluids, atmosphere and ocean dynamics), Tom Hudson (atomistic simulation), Matt Keeling (large-scale simulations), Robert Kerr (fluid dynamics), Markus Kirkilionis (data analysis, machine learning, dynamical systems, bifurctaion theory), Martin Lotz (geometry and complexity), Christoph Ortner, James Sprittles (free surface flows, finite elements), Tim Sullivan (uncertainty quantification, inverse problems)

Brian Bowditch (hyperbolic, riemannian and metric geometry), David Elworthy (global analysis), Mario Micallef (two-dimensional minimal surfaces), Felix Schulze (geometric flows), Peter Topping, Weiyi Zhang (almost complex geometry and symplectic topology)

**DYNAMICAL SYSTEMS & ERGODIC THEORY
**

Claude Baesens, Adam Epstein (complex dynamics in 1D, Tecihmuller theory), Vassili Gelfreich (Hamiltonian systems), Oleg Kozlovski, Robert MacKay, Anthony Manning (hyperbolic systems), Ian Melbourne (smooth ergodic theory; links with probability & stochastic analysis), Joel Moreira (ergodic Ramsey theory), Mark Pollicott (thermodynamic formalism), James Robinson (infinite-dimensional dynamical systems), Caroline Series, Richard Sharp (hyperbolic systems, geodesic flows, thermodynamic formalism), John Smillie (Teichmuller dynamics, complex dynamics in >1D), Colin Sparrow, David Wood

Ergodic Theory & Dynamical Systems seminar

Brian Bowditch (low-dimensional topology, geometric group theory), Emanuele Dotto, John Greenlees (equivariant cohomology, stable homotopy theory, spectral algebra and geometry), Nicholas Jackson (knot theory), Minhyong Kim (arithmetic homotopy theory), Saul Schleimer (low-dimensional topology, geometric group theory), Marco Schlichting (algebraic topology, homotopy theory), Caroline Series (hyperbolic geometry), Richard Sharp (negatively curved spaces, hyperbolic groups, critical exponents), Karen Vogtmann (geometric group theory), Weiyi Zhang (almost complex geometry and symplectic topology)

**MATHEMATICAL, SYSTEMS, & COMPUTATIONAL BIOLOGY (incl. epidemiology)**

Nigel Burroughs, Louise Dyson (cell migration, cancer, epidemiology), Matt Keeling (epidemiology, ecology, evolutionary predictions), Markus Kirkillionis (ecosystems, cell biology, evolution, population dynamics), David Rand, Magnus Richardson, Kat Rock (epidemiology, vector-borne infection, tropical disease elimination), Mike Tildesley (epidemiology, zoonotic disease, disease control)

see also Zeeman Institute for Systems Biology & Infectious Disease Epidemiology Research (SBIDER)

Dwight Barkley, Ed Brambley (acoustics; solid mechanics), Radu Cimpeanu (multi-scale systems, industrial applications), Colm Connaughton (complex systems, industrial applications, data-driven models), Louise Dyson (model simplification), Susana Gomes, Stefan Grosskinsky (stochastic dynamics of complex systems), Tom Hudson (materials science, coarse-graining, stochastic modelling), Matt Keeling (stochastic processes on networks), Markus Kirkilionis (biology, social sciences, economy, finance), Robert MacKay, Magnus Richardson, Kat Rock (ODE, PDE, stochastic, Bayesian fitting), James Sprittles (fluid dyanmics, microflows, interfacial phenomena, industrial applications), Bjorn Stinner (phase field approaches), Florian Theil (materials science, coarse-graining, stochastic modelling), Sebastian Vollmer, Marie-Therese Wolfram

**MATHEMATICAL PHYSICS (incl. STATISTICAL PHYSICS & STATISTICAL MECHANICS)**

Stefan Adams (Gibbs measures; continuum percolation; phase transitions; renormalisation), Siri Chongchitnan (cosmology), Colm Connaughton (kinetic theory, non-equilibrium phenomena), Tobias Grafke (interacting particle systems, lattice gas models), Stefan Grosskinsky (non-equilibrium phase transitions), Minhyong Kim (topological quantum field theory), Roman Kotecky (mathematical statistical physics, phase transitions), Vedran Sohinger (many-body quantum problems), Roger Tribe (random matrix theory), Daniel Ueltschi, Oleg Zaboronski (non-equilibrium statistical mechanics, random matrix theory)

Mathematical Physics and Probability reading seminar

Sam Chow (Diophantine equations and Diophantine approximation), John Cremona (elliptic curves, modular forms, computational number theory), Adam Harper (analytic number theory),Chris Lazda (p-adic cohomology, positive characteristic geometry), Minhyong Kim (Diophantine geometry), David Loeffler (automorphic forms, Iwasawa theory), Martin Orr (arithmetic and Diophantine geometry), Samir Siksek (Diophantine equations, modularity, rational points), Damiano Testa (rational points)

Andreas Dedner (finite element methods, evolution equations), Charles Elliott (finite elements, discretisation, inverse problems), Martin Lotz (numerical optimisation, randomised algorithms), Christoph Ortner, Bjorn Stinner (finite element methods), Tim Sullivan (uncertainty quantification, inverse problems), Marie-Therese Wolfram

**PARTIAL DIFFERENTIAL EQUATIONS**

Radu Cimpeanu (reduced-order modelling, asymptotic analysis), Tom Hudson (calculus of variations, gradient flows, asymptotic methods), Charles Elliott (interfaces & free boundaries; geometric equations; applications incl. biology), Susana Gomes (control theory for PDEs; inverse problems), Xinyu He (Euler equations), Robert Kerr (mathematical fluids – numerical simulations), Christoph Ortner, Filip Rindler (nonlinear and variational), José Rodrigo (fluid mechanics, reaction-diffusion equations, bosons), James Robinson (mathematical fluids – Navier-Stokes equations & MHD), Felix Schulze (geometric PDEs), Vedran Sohinger (nonlinear dispersive PDEs), Florian Theil (nonlinear and variational), Peter Topping (geometric PDEs), Marie-Therese Wolfram

**PROBABILITY & STOCHASTIC ANALYSIS**

Stefan Adams (large deviations, scaling limits (Gaussian free fields); gradient flows; loop measures), David Elworthy (stochastic analysis), Agelos Georgakopoulos (percolation theory, geometric random graphs, random walks), Tobias Grafke (large deviations, rare events), Stefan Grosskinsky (stochastic particle systems, scaling limits), Adam Harper (Gaussian processes and chaos, normal approximation, applications to number theory), Roman Kotecky (probabilitistic discrete maths/phase transitions), Ian Melbourne (connections between ergodic theory & stochastic analysis), Magnus Richardson, Vedran Sohinger (Gibbs measures for nonlinear dispersive PDEs), Tim Sullivan (uncertainty quantification, inverse problems), Roger Tribe (stochastic analysis, interacting particle systems, integrable probability), Daniel Ueltschi, Sebastian Vollmer, Oleg Zaboronski (interacting particle systems, integrable probability), Nikolaos Zygouras

**SET THEORY & FOUNDATIONS OF MATHEMATICS**

**RESEARCH CENTRES and CENTRES FOR DOCTORAL TRAINING**

Centre for Complexity Science (inlcuding the MathSys CDT)

Centre for Doctoral Training in Modelling of Heteregeneous Systems (HetSys CDT)

Centre for Doctoral Training in Mathematics (our PhD programme in Mathematics)

Centre for Discrete Mathematics and its Applications (DIMAP)

Zeeman Institute for Systems Biology & Infectious Disease Epidemiology Research (SBIDER)