Mathematical Sciences

Research

Global Analysis and PDEs

Global Analysis and the theory of partial differential equations are classical fields of mathematics that have a wide range of applications within mathematics, for instance in number theory, group theory, geometry and topology, but also have important applications outside of mathematics to physics, engineering and chemistry.

The Global Analysis and PDEs research group is rooted in pure mathematics and focuses on geometric and topological aspects of analysis. The interests of the group include spectral and scattering theory on manifolds, regularity and existence of global solutions to pseudo-differential equations and boundary value problems, topological questions related to generalizations of the Atiyah-Singer index theorem, applications of theory of PDE to approximation theory, as well as other topics.

Academic staff within the group are:

  • Dr Claudia Garetto: Hyperbolic equations with singularities and/or multiplicities. Well-posedness of weakly hyperbolic equations and systems with multiplicities in Gevrey classes and ultradistribution spaces. Microlocal investigations of the solutions and propagation of singularities. Products of distributions and generalised function algebras (Colombeau).
  • Dr Eugénie Hunsicker: ptic partial differential equations on noncompact and singular manifolds. Intersection Cohomology and its generalizations. Index Theory on noncompact and singular manifolds. Monopole and other moduli spaces arising in physics.

Research students:

  • Joe Cook: properties of the first eigenspace of the Laplacian on hyperbolic surfaces of high symmetry, such as the Bolza surface.