Research Topics

Prospective graduate students can browse through the following in order to gain some idea of what thesis areas they might be able to pursue at Glasgow. See also the research pages and student pages. The named members of staff can be contacted for further details.

- Symmetry and Singularity. The fundamental
question to be addressed here is how the structure of the symmetry
algebra of an ordinary differential equation restricts, and is
restricted by, the singularity structures of its solutions. This
involves a careful discussion of invariants over specific function
fields and methods from Painlevé analysis. (
*Chris Athorne*) - Hirota maps and representation theory. The
aim is to extend results on represesentation theory for sl(2,C) and
sl(3,C) to sl(n.C) and other Lie algebras. In addition to representation
theory the work involves the study of Hilbert-Poincaré series for
homogeneous algebras.(
*Chris Athorne*)

- Adler-Gel'fand-Dickii theory for integrable
lattices. The AGD theory is a unifying framework for the
Hamiltonian stuctures of integrable equations in 1+1 and 1+2 dimensions.
The aim is to incorporate discrete integrable systems of the type
generated by Darboux type transformations.(
*Chris Athorne*and*Jon Nimmo*.)