Our research covers the spectrum of fundamental and applied mathematics.
Algebraic techniques are of central importance in modern mathematics. As such the algebra group sits naturally among a number of major research topics in the department, with connections to geometric topology via group theory, homotopy theory and number theory through representation theory, and algebraic geometry through geometric representation theory.
History of mathematics
History of mathematics is a multidisciplinary subject with close ties to the History Faculty. Research interests cover mathematics and its social context from the early modern period right up to the twentieth century.
Mathematical & computational finance
Due to the multidisciplinary nature of the mathematical finance research, MCFG has strong links and close collaborations with the stochastic analysis group, OCIAM, and the numerical analysis group. The recent upsurge of interest in big data further strengthens such links.
Members of the number theory group work in analytic and combinatorial number theory, arithmetical algebraic geometry, and computational number theory, with numerous and deep connections to current issues in algebra, combinatorics, geometry, topology, logic, and mathematical physics.
The numerical analysis group develops and analyses algorithms for mathematical problems related to partial differential equations, linear algebra, optimization and other areas. The is a strong involvement in applications, with particularly close connections with OCIAM, the Wolfson Centre for Mathematical Biology, and the Centre for Nonlinear PDE.
Oxford Centre for Industrial and Applied Mathematics
Research interests: energy, industry, geoscience, networks, finance, methodologies.
Oxford Centre for Nonlinear Partial Differential Equations
Research focuses on the fundamental analysis of nonlinear PDE, and numerical algorithms for their solution. Current areas of interest include the calculus of variations, nonlinear hyperbolic systems, inverse problems, homogenization, infinite-dimensional dynamical systems, geometric analysis and PDE arising in solid and fluid mechanics, materials science, liquid crystals, biology and relativity.
The members of the topology group have very wide ranging interests in algebraic, geometric and differential topology. Both high- and low-dimensional manifold theory (including knot theory) are represented. Particular research foci are topological quantum field theory and geometric group theory.
Examples case studies articulating the impact of applied mathematics include
- Influencing HIV/AIDS policy in India through mathematical modelling
- Helping the ‘Greeks’ to run faster
- Mathematics in the design and manufacture of novel glass products
- HYDRA: Rolls-Royce's standard aerodynamic design tool
- How networks shape the spread of disease and gossip
- How predictable is technological progress?
- Understanding droplets and surfaces
- Mathematical theories of consciousness
- The Universal Structure of Language