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Mathematical and Statistical Sciences
Dr James Cruickshank
School of Mathematics, Statistic
1009 Arus de Brun
T: Ext. 3965
This is concerned with the geometric and combinatorial mathematics associated with bar and joint frameworks and other related structures. Recently I am interested in connections with polyhedral combinatorics and more general simplicial complexes.
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.
|Project||Start Date||End Date|
|QAYS RASHID SHAKIR EMBASSY OF IRAQ SCHOLARSHIP||21-JUL-14||30-SEP-15|
|HP JAMES CRUICKSHANK TEACHING & LEARNING MATHEMATICS IN A DIGITAL ENVIRONMENT||23-JUN-09||23-MAY-19|
|MF2003 MF86 03 M JAMES CRUICKSHANK||01-SEP-04||20-JUL-07|
Peer Reviewed Journals
|(2022)|| 'Vertex Splitting, Coincident Realisations and Global Rigidity of Braced Triangulations'
James Cruickshank, Bill Jackson and Shin-ichi Tanigawa (2022) 'Vertex Splitting, Coincident Realisations and Global Rigidity of Braced Triangulations'. Discrete & Computational Geometry, [DOI] [Details]
|(2022)|| 'Topological constructions for tight surface graphs'
James Cruickshank, Derek Kitson, Stephen Power, Qays Shakir (2022) 'Topological constructions for tight surface graphs'. Graphs and Combinatorics, [DOI] [Details]
|(2020)|| 'Weil representations via abstract data and Heisenberg groups: A comparison'
Cruickshank, J,Frez, LG,Szechtman, F (2020) 'Weil representations via abstract data and Heisenberg groups: A comparison'. Journal Of Algebra, 547 :129-161 [DOI] [Details]
|(2019)|| 'The rigidity of a partially triangulated torus'
Cruickshank, J,Kitson, D,Power, SC (2019) 'The rigidity of a partially triangulated torus'. Proceedings Of The London Mathematical Society, 118 :1277-1304 [DOI] [Details]
|(2018)|| 'Rigidity of linearly constrained frameworks'
James Cruickshank, Hakan Guler, Bill Jackson, Anthony Nixon (2018) 'Rigidity of linearly constrained frameworks'. International Mathematics Research Notices, [DOI] [Details]
|(2018)|| 'Hermitian and skew hermitian forms over local rings'
Cruickshank, J,Quinlan, R,Szechtman, F (2018) 'Hermitian and skew hermitian forms over local rings'. Linear Algebra And Its Applications, 551 :147-161 [DOI] [Details]
|(2018)|| 'Generators and relations for the unitary group of a skew hermitian form over a local ring'
Cruickshank, J,Szechtman, F (2018) 'Generators and relations for the unitary group of a skew hermitian form over a local ring'. Linear Algebra And Its Applications, 552 :1-28 [DOI] [Details]
|(2017)|| 'Positive polynomials on Riesz spaces'
Cruickshank, J,Loane, J,Ryan, RA (2017) 'Positive polynomials on Riesz spaces'. Positivity, 21 :885-895 [DOI] [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, 25 :1403-1409 [DOI] [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]
|(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]
|(2014)|| IADIS International Conference on Intelligent Systems & Agents
Christine Marshall, Colm O'Riordan, James Cruickshank (2014) Investigating Properties of Random Geometric Graphs IADIS International Conference on Intelligent Systems & Agents [Details]
|(2018)|| Big Data Analytics, Data Mining & Computational Intelligence
Christine Marshall, Colm O'Riordan, James Cruickshank (2018) IDENTIFYING A GAME-THEORETIC TRANSITION THRESHOLD ON HYPERBOLIC NETWORKS Big Data Analytics, Data Mining & Computational Intelligence [Details]
|(2017)|| European Network Intelligence Conference
Christine Marshall, Colm O'Riordan, James Cruickshank (2017) Targeting influential nodes for recovery in bootstrap percolation on hyperbolic networks European Network Intelligence Conference [Details]
|(2020)|| Graph Drawing and Network Visualization
James Cruickshank and Qays Shakir (2020) Contacts of Circular Arcs Representations of Tight Surface Graphs . In: Auber, David and Valtr, Pavel eds. Graph Drawing and Network Visualization Vancouver, , pp.529-531 [Details]
|(2018)|| 2018 IEEE/ACM INTERNATIONAL CONFERENCE ON ADVANCES IN SOCIAL NETWORKS ANALYSIS AND MINING (ASONAM)
Marshall, C;Cruickshank, J;O'Riordan, C (2018) Identifying Influential Nodes to Inhibit Bootstrap Percolation on Hyperbolic Networks 2018 IEEE/ACM INTERNATIONAL CONFERENCE ON ADVANCES IN SOCIAL NETWORKS ANALYSIS AND MINING (ASONAM) , pp.1266-1273 [Details]
|(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]
|(2021)|| Software for computing irreducible (2, 2)-tight torus graphs.
James Cruickshank, Qays Shakir (2021) Software for computing irreducible (2, 2)-tight torus graphs. Computer Program [Details]
|(2022)|| Global Rigidity of Line Constrained Frameworks.
James Cruickshank, Fatemeh Mohammadi, Harshit J. Motwani, Anthony Nixon, Shin-ichi Tanigawa (2022) Global Rigidity of Line Constrained Frameworks. Electronic Publication [Details]
|(2020)|| Symmetric contact systems of segments, pseudotriangulations and inductive constructions for corresponding surface graphs.
James Cruickshank, Bernd Schulze (2020) Symmetric contact systems of segments, pseudotriangulations and inductive constructions for corresponding surface graphs. Electronic Publication [Details]
|(2021)|| Braced triangulations and rigidity.
James Cruickshank, Eleftherios Kastis, Derek Kitson, Bernd Schulze (2021) Braced triangulations and rigidity. Electronic Publication [Details]
|(1999)|| Twisted cobordism and its relationship to equivariant homotopy theory.
James Cruickshank (1999) Twisted cobordism and its relationship to equivariant homotopy theory. Thesis [Details]
|Association||Function||From / To|
|Irish Mathematical Society||President||01-JAN-10 / 31-DEC-11|
|Employer||Position||From / To|
|University College Cork||Lecturer||01-SEP-98 / 31-AUG-01|
|Title||Type||From / To|
|Teaching (e.g. Service learning / comunity based learning)||Mathematical Enrichment Programme||01-JAN-02 / 15-JUN-17|
I am a member of the editorial board of the Bulletin of the Irish Mathematical Society
I am interested in the role of problem solving as a driver of learning in mathematics. Undergraduate mathematics faces special challenges in implementing a research-led approach. Due to the highly abstract and technical nature of contemporary research in many (but not all!) mathematical disciplines it can often be difficult to introduce undergrad students to open problems in contemporary mathematics. However there is a rich tradition of mathematical problem solving that can provide a bridge. Throughout my career at NUI Galway I have tried to promote student interest in problem solving contest at all levels. In particular
- The mathematical enrichment programme seeks to engage preuniversity students in extracurricular mathematics with a particular focus on preparing for so-called Olympiad contests such as the Irish Mathematical Olympiad and the International Mathematical Olympiad. I been heavily involved in the administration and teaching of this course for the last 15 years.
- The PRISM contest is also for preuniversity students and is one of the largest one day mathematical contests in Ireland with typically 4000-5000 students participating. I was one of the founders of this contest and have been responsible for maintaining and upgrading its website for the last 10 years.
E-assessment in mathematics
I am very interested in using new technologies to support learning. Mathematics is a subject that offers particular opportunity to support student learning with automated assessment technologies. In recent years, several new developments contributed to an rapid growth in the area of mathematical e-assessment. In particular
- MathJax essentially solved the problem of presenting complex mathematical notation on the web
- Open source computer algebra systems such as SageMath and Maxima have advanced to a high level of sophistication - comparable to state of the art systems such as Mathematics/Maple.
- Widespread student access to the web through a variety of devices and platforms
- Web development in general has changed dramatically in the last decade. The latest web development frameworks have made it much easier to develop sophisticated/responsive applications without requiring a large team of developers
I have used this system successfully in the last two academic years, both for large group teaching to first year service courses and for more specialised courses in actuarial mathematics for third year students. I plan to roll out the system to several other courses in the 2017-18 academic year.
for a talk that I gave about this system at the E-Assessment in Mathematical Sciences conference at Newcastle University in September 2016.
Recent Postgraduate Students
|Term/Year||Module Title||Module Code||Subject / Desc|
|2022/23 semester 2||Advanced Group Theory||MA4344|
|2022/23 semester 2||Software for Mathematical Scientists and Educators||CS3101|
|Name||Description of Collaboration|
Random geometric graphs in evolutionary game theory
|Name||Organisation / Institute||Country||Description of Collaboration|
|Derek Kitson||Lancaster University||UNITED KINGDOM||
Geometric rigidity theory
|Anthony Nixon||Lancaster University||UNITED KINGDOM||
|Bill Jackson||Queen Mary, London||UNITED KINGDOM||
|Bernd Schulze||Lancaster University||UNITED KINGDOM||
|Shnichi Tanigawa||University of Tokyo||JAPAN||
|Steve Power||Lancaster University||UNITED KINGDOM||
Geometric rigidity theory
|Fernando Szechtman||University of Regina||CANADA||
Linear and multilinear algebra over local rings