The CDT offers a 4-year DPhil programme with the central aim of producing highly trained, outstanding mathematicians with deep expertise and interdisciplinary skills in the analysis and applications of Partial Differential Equations (PDEs) and related areas of core mathematics and its interfaces.
The first year consists of a foundation module, core courses and two 10-week mini-projects in different areas of research with the purpose of both developing knowledge and helping to decide on a suitable research topic. There are also Topical courses and a regular seminar series to advise of the latest advances in related research.
Partial Differential Equations
PDEs are at the heart of many scientific advances. The behaviour of every material object in nature, with time scales ranging from picoseconds to millennia and length scales ranging from sub-atomic to astronomical, can be modelled by deterministic and stochastic PDEs or by equations with similar features. Indeed, many subjects revolve entirely around their underlying PDEs, including:
• Fluid dynamics: the Euler equations and the Navier-Stokes equations;
• Electrodynamics, optics and electric circuits: Maxwell’s equations;
• Nonequilibrium statistical mechanics: the Boltzmann equation;
• Quantum mechanics: the Schrödinger equation;
• Cosmology: the Einstein equations of general relativity.
The role of PDEs within mathematics (especially nonlinear analysis, geometry, topology, stochastic analysis, numerical analysis, and applied mathematics) and in other sciences (such as physics, chemistry, life sciences, climate modelling/prediction, materials science, engineering, and finance) is thus fundamental and is becoming increasingly significant. At the same time, the demands of applications have led to important developments in the analysis of PDEs, which have in turn proved valuable for further different applications.