Graduate Studies

School of Mathematics, Statistics and Applied Mathematics

The Department of Mathematics carries out research in Algebra, Analysis, Geometry/Topology, and Statistics. Details are given on the Department's research page.

Details of the research interests of the Department of Applied Mathematics are available here.

For further information on the School of Mathematics, Statistics and Applied Mathematics click here.

Recent PhDs

Dr. Seamus Gerard Kelly
Thesis Title: Combinatorial Polytopes and Group Cohomology
Summary: Polytopes are higher dimensional generalisations of the classical 3-dimensional polyhedra. In this thesis, finite groups of symmetries are used to generate examples of polytopes. From the polytopes homological properties of the groups are computed. The methods are implemented as computer programs and applied to several families of finite groups.

Dr. Patrick Browne
Thesis Title: On Abelian Ideals in a Borel Subalgebra of a Complex Simple Lie Algebra
Summary: This thesis makes a major contribution to two hitherto unrelated areas of current research in differential geometry; the study of abelian ideals in complex simple Lie algebras and construction of Einstein manifolds. The uniform method of the thesis for completely describing the abelian ideals leads to an intriguing connection with noncompact Einstein solvmanifolds. The dimension formulas for the abelian ideals also give the eigenvalue type of the corresponding Einstein solvmanifold.

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