Research Interests

At the moment I am thinking about rigidity theory, in the sense of bar and joint frameworks various other related structures. I am also thinking about a problem related to automorphisms of directed graphs.

I have also recently been interested in linear spaces of nilpotent matrices and in unitary groups over finite local rings.

A long time ago, I wrote my thesis on homotopy theory, and I am still interested in topology.

Papers and preprints

Here are my arXiv preprints and here is my MathSciNet listing.

Miscellania

Here are the slides for a talk that I gave at a workshop on Geometric and Topological Graph Theory that was held at Bristol University in April 2013. Here are the slides of an introductory talk on rigidity theory that I gave at NUI Galway just before the Bristol conference.

I gave a talk on spaces of nilpotent matrices at the DeBrun workshop on Linear Algebra, Matrix Theory and Applications in December 2012 - the slides are here.

Postgraduate Supervision

Two students have completed their PhD under my supervision.

Seamus Kelly (co supervised with Graham Ellis). Combinatorial Polytopes and Group Cohomology.
Jonathan McLaughlin. Moduli Spaces of Planar Realizations of Weighted Graphs.

At the moment I am cosupervising (with Colm O'Riordan) Christine Marshall - she is writing a PhD thesis which involves some work on random geometric graphs. I am not currently supervising any research students and I would be interested in hearing from any potential candidates. You can find some information (including information on possible sources of funding) about the research degree programmes in the School of Maths here.