Numerical approximation of PDEs, Computational Science and Engineering, Parallel Scientific Computing, Numerical Linear Algebra.
Santiago Barrera Acevedo
Algebraic design theory, cocyclic Hadamard matrices, relative difference sets, correlation of finite arrays, and other combinatorial designs.
Functional analysis, harmonic analysis, geometric analysis, elliptic and parabolic PDEs, variational calculus.
Mixed Integer Programming, Algorithm performance analysis, Optimisation applications, Operations research.
Solar physics, magnetohydrodynamics, helioseismology, MHD waves.
Evolution of nonlinear waves in geophysical fluid dynamics, numerical modelling meteorology, modeling density-stratified fluids.
Eigenvalues, parabolic equations, heat flow, geometric analysis, calculus of variations, geometric evolution equations, mean curvature flow.
Stochastic processes, large deviations and applications to statistical mechanics, random graph theory, self-interacting random processes, urn models.
Computational inverse problems; Uncertainty quantification; Model reduction; Machine learning; Computational geophysics; Subsurface flows.
Mathematical physics, High-speed fluid flows, asymptotic analysis, nonlinear PDEs (Naiver-Stokes equations), dynamical systems theory picture of turbulence.
Computational algebra, in particular, group theory, Lie theory, and some aspects of algebraic design theory.
Geometry, topology, combinatorics and mathematical physics, enumerative geometry, moduli spaces of curves, Gromov-Witten theory, graphs on surfaces, matrix models and topological recursion.
Solar Physics, Applied Mathematics for Helioseismology, Solar flares, Machine Learning Data Applications and solar quakes.
Numerical methods for elliptic and parabolic PDEs, polytopal meshes, high-order methods, finite volume methods, convergence analysis, compactness techniques.
Operations Research, Integer Programming, Meta-heuristics, Applications of optimisation in logistics, mining & rostering.
Theoretical and Empirical Asset pricing, financial econometrics, machine learning.
Applied mathematics, Mathematical modelling, Applied stochastic processes, multiscale modelling and Mathematical biology.
Symplectic and contact geometry.
Mathematical physics, statistical mechanics, combinatorics (probability on graphs), Markov chain Monte Carlo methods.
Financial mathematics, stochastic control, optimal transport, model calibration, robust finance, stochastic games, graph theory, machine learning.
Harmonic/Fourier analysis, nonlinear PDEs of dispersive type and Fluid dynamics
Applied Mathematics, nonlinear stability theory, turbulence.
Dynamical systems and ergodic theory. Interactions between geometry, topology, and dynamics.
Deputy Head of School
General theory of stochastic processes, representation properties for martingales, markov jump processes, applications of stochastic processes to modelling of financial markets.
Topology and geometry, symplectic and contact geometry, holomorphic curves, low dimensional topology.
Combinatorial designs and edge decompositions of graphs, especially embedding, colouring and matching problems for block designs and cycle decompositions of graphs.
Graphs, matroids, and combinatorial optimization.
Analytic methods in enumerative combinatorics, generating functions, asymptotic analysis, random graphs and hypergraphs.
Random graphs and processes, Ramsey theory, extremal combinatorics.
Bayesian modelling and computational methods, bioinformatics, invasive species modelling and epidemiology.
Stochastic processes, probability; stochastic models, populations models, financial mathematics, volatility, market models, martingales, random perturbations, applied probability.
Theoretical and numerical analysis of stochastic partial differential equations, anomalous sub-diffusion equations.
Optimal transport, Financial mathematics, Non-linear PDE's, Monge-Ampere equation.
Complex analysis, graph theory, probability.
Alberto F. Martin
Scientific Computing, Partial Differential Equations, Finite Elements, High Performance Scientific Computing.
Low-dimensional topology, knot theory, contact and symplectic topology, hyperbolic geometry, Heegaard Floer homology, mathematical physics, topological quantum field theory, and their algebraic, geometry, and combinatorics.
Stochastic control, controllable Markov chains, dynamic programming, Markov decision problems.
Backward stochastic differential equations, optimal control of random systems such as dynamic random network, stochastic differential game, and their application to finance and biology.
Probability and random processes on discrete structures.
Partial differential equations, singular limits of symmetric hyperbolic systems, geometric PDE's, general relativity, Newtonian limit, post-Newtonian expansions, Einstein-Yang-Mills, gravitating perfect fluids and elastic bodies, geometric flows, Ricci flow, renormalization group flow.
Geometry and Lie theory: invariant geometric structures on manifolds, Lie groups, solvmanifolds, Lie algebras.
Finite and topological geometry, combinatorial designs, group theory, history of mathematics, classical interpolation theory, computer visualisation, mathematics education and outreach.
Low-dimensional topology and geometry.
Smooth Ergodic Theory, Parabolic Dynamics, Partially Hyperbolic Dynamics.
Control theory, numerical dynamics, optimisation, convex and set-valued analysis.
Spatial statistics, multivariate statistics, data assimilation.
Ricardo Ruiz Baier
Numerical analysis of PDEs, mixed finite element methods, modelling of multiphase flow in porous media, large solid deformations, cardiac electromechanics.
Nonlinear Partial Differential Equations, calculus of variations.
Cloud physics, Boundary layer meteorology, Weather modification.
Theoretical, numerical, and experimental fluid dynamics, especially relevant to geology and industrial processes.
Machine learning, combinatorial optimisation, operations research, mathematical programming, meta-heuristics.
Mathematical modelling of complex biological systems, including genetic regulatory networks, cell signalling transduction pathways, and cancer therapy. Inference of complex networks from big data.
Retirement income product design and pricing, portfolio optimisation, derivatives pricing and risk management.
Head of School
Dynamical systems, Chaos theory, Computer-assisted proofs, Artificial intelligence.
Geometric singular perturbation theory; Canard theory; Dynamical systems; Spiking and bursting in excitable cells; Mixed-mode oscillations; Neuronal signalling; Early afterdepolarisations in cardiomyocytes.
Latin squares and other combinatorial matrices; quasigroups, matrix permanents, graph theory (matchings, factorisations, random graphs), enumeration algorithms for combinatorial objects.
Discrete mathematics and theoretical computer science, especially structural graph theory, extremal graph theory, geometric graph theory, graph colouring, poset dimension, graph drawing, and combinatorial geometry.
Random structures and probabilistic combinatorics, graph theory, enumeration of graphs and maps, asymptotic enumeration and minimal Steiner trees. Solving combinatorial problems using real and complex analysis, probability and stochastic processes, and generating functions.
Applied probability, Statistical Mechanics, Markov chain Monte Carlo methods.