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Mathematics, Statistics & Applied Mathematics

Dr James Cruickshank

PhD

Contact Details

Lecturer Above The Bar
------------------------
Room ADB-1009
Áras De Brún
School of Mathematics, Statistics and Applied Mathematics

T: Ext. 3965
E: james.cruickshank@nuigalway.ie
 
researcher

Biography

I studied at UCG from 1988 to 1993 obtaining a B.Sc (Mathematics) and an M.Sc. (Mathematics). Following that I obtained my PhD from University of Alberta in 1999 under the supervision of Prof George Peschke. I have been a lecturer at NUI Galway since September 2001

Research Interests

Geometric Rigidity Theory
This is concerned with the geometric and combinatorial mathematics associated with bar and joint frameworks and other related structures. In particular I have worked on 3D rigidity of bar and joint frameworks and rigidity theory of surface graphs and of block-and-hole graphs. Collaborators: Steve Power (Lancaster University), Derek Kitson (Lancaster University), Qays Shakir (NUI Galway)

Linear and multiilinear algebra over local rings
Local rings arise naturally in several mathematical contexts. We have studied hermitian and skew hermitian forms over such rings and proved several new classification theorems for such forms. We have also investigated analogues of the classical matrix groups in this context. Collaborators: Fernando Szechtman (University of Regina), Rachel Quinlan (NUI Galway)

Random geometric graphs 
We have investigated the use of random geometric graphs to model networks in evolutionary game theory and related areas. Collaborators: Colm O'Riordan (NUI Galway), Christine Marshall (NUI Galway)

Peer Reviewed Journals

  Year Publication
(2016) 'Positive polynomials on Riesz spaces'
Cruickshank, J., Loane, J. & Ryan, R.A. (2016) 'Positive polynomials on Riesz spaces'. Positivity, [DOI] [Details]
(2017) 'The generic minimal rigidity of a partially triangulated torus'
James Cruickshank, Derek Kitson, Stephen Power (2017) 'The generic minimal rigidity of a partially triangulated torus'. Proceedings Of The London Mathematical Society, [Details]
(2017) 'The generic rigidity of triangulated spheres with blocks and holes'
Cruickshank, J,Kitson, D,Power, SC (2017) 'The generic rigidity of triangulated spheres with blocks and holes'. Journal Of Combinatorial Theory Series B, 122 :550-577 [DOI] [Details]
(2014) 'The smooth structure of the moduli space of a weighted series-parallel graph'
Cruickshank, J,McLaughlin, J (2014) 'The smooth structure of the moduli space of a weighted series-parallel graph'. Topology And Its Applications, 164 :242-247 [DOI] [Details]
(2014) 'Unitary groups over local rings'
Cruickshank, J,Herman, A,Quinlan, R,Szechtman, F (2014) 'Unitary groups over local rings'. Journal Of Algebra And Its Applications, 13 [DOI] [Details]
(2014) 'On Spaces of Infinitesimal Motions and Three Dimensional Henneberg Extensions'
Cruickshank, J (2014) 'On Spaces of Infinitesimal Motions and Three Dimensional Henneberg Extensions'. Discrete & Computational Geometry, 51 :702-721 [DOI] [Details]
(2011) 'Series Parallel Linkages'
Cruickshank, J,McLaughlin, J (2011) 'Series Parallel Linkages'. Publicacions Matematiques, 55 :359-378 [Details]
(2007) 'Software for calculating blood lactate endurance markers'
Newell, J ; Higgins, D; Madden, N; Cruickshank, J; Einbeck, J; McMillan, K; McDonald, R (2007) 'Software for calculating blood lactate endurance markers'. Journal Of Sports Sciences, [Details]
(2006) 'Rearrangement inequalities and the alternahedron'
Cruickshank, J,Kelly, S (2006) 'Rearrangement inequalities and the alternahedron'. Discrete & Computational Geometry, 35 :241-254 [DOI] [Details]
(2003) 'Twisted homotopy theory and the geometric equivariant l-stem'
Cruickshank, J (2003) 'Twisted homotopy theory and the geometric equivariant l-stem'. Topology And Its Applications, 129 :251-271 [DOI] [Details]

Book Chapters

  Year Publication
(2008) 'Functional Equations'
James Cruickshank, Gary McGuire, Anthony G. O'Farrell, David B. Redmond, Richard O. Watson and David J. Wraith. Edited by Anthony G. O'Farrell. (2008) 'Functional Equations' In: Irish Mathematical Olympiad Manual. Maynooth, Ireland: Logic Press. [Details]

Edited Books

  Year Publication
(2005) Bulletin of the Irish Mathematical Society: Special edition.
James Cruickshank, Dane Flannery (Ed.). (2005) Bulletin of the Irish Mathematical Society: Special edition. Ireland: Irish Mathematical Sociey. [Details]

Electronic Publication

  Year Publication
(2017) Unitary groups and ramified extensions.
J. Cruickshank, F. Szechtman (2017) Unitary groups and ramified extensions. Electronic Publication [Details]
(2017) Hermitian and skew hermitian forms over local rings.
James Cruickshank, Rachel Quinlan, Fernando Szechtman (2017) Hermitian and skew hermitian forms over local rings. Electronic Publication [Details]