Dr Thomas McCourt
Profiles

Dr Thomas McCourt

Lecturer in Pure Mathematics

School of Computing, Electronics and Mathematics (Faculty of Science and Engineering)

Role

I am a lecturer in pure mathematics at the School of Computing, Electronics and Mathematics. .

My research interest lie in topics such as Topological Graph Theory, Algebraic Structures arising from Combinatorial Designs, Metric Geometry, and experimental designs related to modelling and simulation.

This academic year I am teaching on the final year modules Geometry and Algebra, and Optimisation, Networks and Graphs; the first year module Linear Algebra and Complex Numbers; and the foundation year module Applied Mathematics.

Qualifications

PhD - University of Queensland

BSc (Hons) - University of Queensland

Teaching interests

I am currently teaching on the final year modules: Geometry and Algebra, and Optimisation, Networks and Graphs; the first year module Linear Algebra and Complex Numbers; and the foundation year module Applied Mathematics

Over the last two years I have taught on the final year module: Geometry and Topology, the first year module: Linear Algebra and Complex Numbers and the foundation year modules: Mathematics for Extended Science and Applied Mathematics.

I have also taught at other universities in Australia, the US and the UK and have delivered invited post-graduate lecture series in Thailand as part of the CIMPA research school program.

My teaching experience covers all year levels including student research project supervision and post-graduate courses.

I have also been involved in a number of outreach programs running workshops for high school students and giving lectures to the general public.


Research interests

My research interests lie where the field of combinatorics intersects other areas of mathematics. My ongoing research projects include the following.
  • Metric Geometry: in particular problems related to the rigidity of frameworks on surfaces.
  • Algebraic structures arising from Combinatorial Designs.
  • Topological Graph Theory: in particular closed 2-cell embeddings.
  • Experimental Design: using a combination of analysis, statistics and combinatorics to evaluate the suitability of experimental designs for use in industry.


Submitted
  • T.A. McCourt, 'Growth rates of groups associated with face 2-coloured triangulations and directed Eulerian digraphs on the sphere'. (arXiv.)
  • T.A. McCourt and J.Z. Schroeder, 'Self-embeddings of doubled affine Steiner triple systems'.
  • K. Burrage, P. Burrage, D.M. Donovan, T.A. McCourt, H.B. Thompson, and E.S. Yazici, 'Estimates of the coverage of parameter space by Latin Hypercube and Orthogonal sampling: connections between Populations of Models and Experimental Designs'.

In press
  • D.M. Donovan, T.S. Griggs, T.A. McCourt, J. Opršal and D. Stanovský, 'Distributive and anti-distributive Mendelsohn triple systems', Canadian Mathematical Bulletin, in press. (arXiv.)

Published
  • T.S. Griggs and T.A. McCourt, 'Biembeddings of symmetric n-cycle systems', Graphs and Combinatorics, 32 (2016), 147-160.
  • D.M. Donovan, T.S. Griggs, J.G. Lefevre and T.A. McCourt, 'Further biembeddings of twofold triple systems', Ars Mathematica Contemporanea, 8 (2015), 267-273. (Link.)
  • S. R. Blackburn and T.A. McCourt, 'Triangulations of the sphere, bitrades and abelian groups', Combinatorica, 34 (2014), 527-546. (arXiv.)
  • B. Jackson, A. Nixon and T.A. McCourt, 'Necessary conditions for the generic global rigidity of frameworks on surfaces', Discrete & Computational Geometry, 52 (2014), 344-360. (arXiv.)
  • T.A. McCourt, 'Biembedding a Steiner triple system with a hamilton cycle decomposition of the complete graph', Journal of Graph Theory, 77 (2014), 68-87. (Link.)
  • M.J. Grannell and T.A. McCourt, 'Doubly even orientable closed 2-cell embeddings of the complete graph', Electronic Journal of Combinatorics, 21 (2014). (Link.)
  • D. M. Donovan, T.S. Griggs, J.G. Lefevre and T.A. McCourt, 'Cyclic biembeddings of twofold triple systems', Annals of Combinatorics, 18 (2014), 57-74.
  • K. Burrage, P. Burrage, D. Donovan, T. McCourt and B. Thompson 'Estimates on the coverage of parameter space using populations of models', Modelling and Simulation, IASTED, ACTA Press (2014).
  • G. Martin and T.A. McCourt, 'Small embeddings for partial 5-cycle systems', Journal of Combinatorial Designs, 20 (2012), 199-226. (Link.)
  • N.J. Cavenagh, D.M. Donovan, A. Khodkar, J.G. Lefevre and T.A. McCourt, 'Identifying flaws in the security of critical sets in latin squares via triangulations', The Australasian Journal of Combinatorics, 52 (2012), 243-268.
  • N.J. Cavenagh, D.M. Donovan, J.G. Lefevre and T.A. McCourt, 'Distinct equilateral triangle dissections of convex regions', Commentationes Mathematicae Universitatis Carolinae, 53 (2012), 189-210.
  • D.M. Donovan, E.J. Billington, J.G. Lefevre, T.A. McCourt and C.C. Lindner, 'The triangle intersection problem for nested Steiner triple systems', The Australasian Journal of Combinatorics, 51 (2011), 221-234.
  • D.M. Donovan, M.J. Grannell, T.S. Griggs, J.G. Lefevre and T.A. McCourt, 'Self-embeddings of cyclic and projective Steiner quasigroups', Journal of Combinatorial Designs19 (2011), 16-27. (Link.)
  • J.G. Lefevre and T.A. McCourt, ' The Disjoint m-Flower Intersection Problem for Latin Squares', Electronic Journal of Combinatorics, 18 (2011). (Link.)
  • T.A. McCourt, 'The intersection problem for disjoint 2-flowers in Steiner triple systems', Journal of Combinatorial Mathematics and Computing, 75 (2010), 41-63.
  • T.A. McCourt, 'On defining sets in latin squares and two intersection problems, one for latin squares and one for Steiner triple systems', Bulletin of the Australian Mathematical Society, 82 (2010), 351-352. (Link.)

Invited Speaker:
  • Face 2-coloured triangulations and directed Eulerian digraphs on the sphere. Pure Mathematics Seminar Series, Lancaster University, UK, 2015.
  • Properly face two-coloured spherical triangulations: their canonical groups and recursive constructions. British Mathematical Colloquium: Combinatorics Workshop, QMUL, UK, 2014.
  • Distributive and anti-distributive Mendelsohn quasigroups. Combinatorics Seminar Series, University of Bristol, UK, 2013.
  • Lecture series on spherical latin bitrades. (Two 80 minute lectures.) CIMPA 2013 Graduate School: Graphs, Codes and Designs, Bangkok, Thailand, 2013.
  • Lecture series on (v,k,λ) designs. (Three 80 minute lectures.) CIMPA 2013 Graduate School: Graphs, Codes and Designs, Bangkok, Thailand, 2013.
  • Face two-colourable triangulations of the sphere and abelian groups. Mathematics Seminar Series, Nottingham Trent, UK, 2013.
  • Biembedding designs and minimum genus embeddings. SIAM Conference on discrete mathematics Mini-symposium: Graphs on Surfaces, Halifax, Canada, 2012.
  • Biembedding twofold triple systems. Open University Winter Combinatorics Meeting, Open University, UK, 2011.