Geometry and Analysis

Geometry research at York includes: Differential Geometry including harmonic maps and sections; variational theory of Riemannian G-structures; integrable surface theory (minimal surfaces, CMC surfaces, Willmore surfaces); Geometric Group Theory including the interplay between groups and manifolds, particularly in hyperbolic geometry; Geometric Invariant Theory including the theory of invariants of linear algebraic groups acting on algebraic varieties.  Our analysts are active in functional analysis, operator theory and harmonic analysis, and in applications of analysis to integral and differential equations and signal processing. We also have expertise in probabilistic methods in Dynamical Systems and Ergodic Theory.



Photo: phila4 by fdecomite, licensed under CC BY 2.0

PhD Projects

Prospective students are warmly invited to email staff to discuss potential projects, so that we can ensure the best fit between staff and students.

Information about the application process and funding opportunities can be found at the Research courses: MSc, PhD, MPhil page.

Staff supervising projects in this area are:

  • Dr Zaq Coelhointerplay between Probability Theory and Dynamical Systems, which is commonly known as Ergodic Theory. Deciding which measure(s) best describes the chaotic behaviour of the trajectories of a dynamical system is one of the scopes of Ergodic Theory
  • Dr Ian McIntoshminimal surfaces and harmonic maps from surfaces into symmetric spaces.  In particular, moduli spaces of minimal surfaces studied via HIggs bundles, and the application of minimal surface theory to the problem of parameterising "good" representations of a surface group (fundamental group of a surface) into non-compact simple Lie groups.
  • Dr Graeme Wilkin: I am interested in the topology and geometry of moduli spaces that arise in gauge theory, such as moduli spaces of Higgs bundles and quiver varieties. These spaces have a very rich structure and a number of surprising connections to other areas of mathematics and physics, such as mirror symmetry, Geometric Langlands and representations of quantum affine algebras.

Projects in analysis are also offered by members of the Mathematical Finance and Stochastic Analysis Research Group. Projects of a geometric flavour are also offered by Eli Hawkins (Mathematical Physics)