Dr Graham Roberts

Senior Lecturer

Gained a first class honours in Mathematics from the Open University in 1988, a PGCE in 1989 and a PhD from Liverpool  University in 2001.

Qualifications

B.Sc,  B.A.(Hons), PhD, PGCE.

Overview

Graham has spent 16 years as an Open University tutor and also worked at the John Moores International Study Centre and at Edge Hill University.

All Graham’s mathematics qualifications have been gained whilst in full-time employment.

Member of the London Mathematical Society.

Teaching

Graham has taught at all the undergraduate levels and at Masters level including Masters supervision.

Research

Algebraic Topology/ Cohomology/Differential Geometry.

  • Differential forms as F-relative Hochschild cochains.
  • Div, grad and curl as cochains using a flat connection.
  • Structure functions leading to a ‘Taylor’ series for F-relative cochains.
  • The isomorphism between the complex of F-relative cochains of differential operators and the jets of the Alexander-Spanier complex.
  • Proof that not all morphisms from the de Rham complex to the Alexander complex derive from a class of geodesics.
  • Proof of the isomorphism of the Hochschild complex and the F-relative Hochschild complex.
  • The transfer of properties of differential forms to Alexander cochains. and Hochschild cochains, including the Cartan homotopy relation.
  • A generalisation of the Lie derivative from vectors and p-forms to differential operators.
  • Discovery of an exact sequence of Christoffel symbols and its relationship to path equivalent connections on a manifold.

Published work

Articles

  • ‘The Structure of F-Tensorial Cochains’, Differential Geometry and its Applications, North Holland. (1999).
  • ‘An Introduction to Cochains of Differential Operators’,  Banach Centre Publications,  Institute of Mathematics, Polish Academy of Sciences. (2003).
  • (with Y.Yan and Kamal Pal) ‘Finite difference method for two-sided space fractional partial differential equations’, Proceedings of the Sixth Conference on Finite Difference Methods, Lozenetz. Elsevier. (2014)

Graham’s research has also been presented at workshops and seminars in several European universities