Mathematics, dynamical systems and PDEs

As a PhD student in the School of Mathematics and Physics you will work as part of a vibrant and supportive community of early career researchers who exchange ideas and collaborate with each other and the mathematical community. You will be extensively trained for a career as a professional mathematician, which will set you on the right track for a future in academia, industry or government.

During your PhD you will also receive a comprehensive training in transferable skills such as project management, communication and time management through our Faculty Graduate School. In addition, you will broaden your mathematical horizons by taking courses via national networks such as the national MAGIC consortia as well as our own in-house MSc course.

About the group

The Dynamical Systems and Partial Differential Equations Group's work is essential in the underpinning of the research in more applied areas carried out by other groups in the School (the Biosystems and the Nonlinear Waves and Geometric Fluid Dynamics Group), and enjoys collaborative relationships with universities around the world in locations such as Brazil, Argentina, the United States, Italy and South Korea.

Maths at Surrey has a strong reputation in the area of dynamical systems and analysis of nonlinear PDEs; thus dynamical systems has been the focus of the group for a long time. Sub-areas where this group is active include:

• Analysis of Hamiltonian, dissipative and delayed PDEs arising in fluid dynamics, material sciences and pattern formation
• Perturbation theory (regular and singular) and bifurcation analysis of Hamiltonian systems and near Hamiltonian systems
• Numerics of differential equations, numerical bifurcation analysis
• Calculus of variations and nonlinear elasticity theory.
• Ergodic theory and its applications to mathematical analysis.

Potential PhD research

Potential topics of PhD research include:

• Well-posedness, regularity and blow up of solutions
• Justification of singular limits, for example, averaging and homogenization problems
• Long-time behaviour of dynamical systems, such as attractors, finite-dimensional reduction, inertial manifolds, space-time chaos, length scales, and sharp estimates
• Analysis of time-semi-discretizations of nonlinear evolution equations
• Dynamical systems analysis of fronts, solitary waves, rolls or spots.

Further topics could be available by contacting individual group members.

Applicants should have:

• A minimum of a first-class honours degree in mathematics, physical sciences or engineering.

Preferably applicants will hold:

• A MMath, MPhys or MSc degree, though exceptional BSc students will be considered.