## Contents

- Links to my research on other sites
- Refereed research articles
- Other publications and work in progress
- Slides from selected presentations
- Projects by research students
- Theses, code, data, and appendices

## Links to my research on other sites

- MathSciNet (subscription required)
- arxiv.org
- ResearchGate
- ExpertGuide
- Facebook group: Australia-Vietnam Free Trade Network
- Twitter: @AustVNFreeTrade

## Refereed research articles

Note: Clicking on the journal name will link to the final published version, which may require a subscription. Clicking on the article name will link to the last preprint version.

- With Julio Romero,
**An algebraic and combinatorial approach to the construction of Experimental Designs**,*International Journal of Geotechnique, Construction Materials and Environment (GEOMATE)***12**(2017), no 29, 66-72. doi.org/10.21660/2017.29.1308 - With Tai Huu Pham,
**Australia and New Zealand: Potential impact on ASEAN growth**, accepted by*Vietnam Social Sciences Review*, Vietnam Academy of Social Sciences. - With Julio Romero,
**Enumeration of Strength Three Orthogonal Arrays and Their I****mplementation in Parameter Design**,*Journal of Applied Mathematics and Physics***3**(2015), no. 1, 38-45. - With Lisa Carbone and Hisham Sati,
**Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories**,*Journal of Mathematical Physics*56 no. 10, 103501 (2015). dx.doi.org/10.1063/1.4929538 arXiv:1407.3370 - With Man V. M. Nguyen,
**Enumeration of strength****3 mixed orthogonal arrays**,*Southeast Asian Journal of Sciences***1**(2012), no. 2, 155-168. - With Lisa Carbone and Leigh Cobbs,
**Fundamental domains for congruence subgroups of**SL_{2}**in positive characteristic**,*J. Algebra***325**(2011), 431-439. arXiv:0909.0062 - With Colva M. Roney-Dougal,
**Constructive homomorphisms for classical groups**,*J. Symbolic Comput.***46**(2011), no. 4, 371-384. arXiv:1009.1672 - With Arjeh M. Cohen,
**An algorithm for Lang’s Theorem**,*Journal of Algebra***322**(2009) no. 3, 675-702. arXiv:math/0506068.

Additional material below. - With Arjeh M. Cohen and Sergei Haller,
**Computing in unipotent and reductive algebraic groups**,*LMS Journal of Computational Mathematics***11**(2008), 343-366. arXiv:math/0611013 - With Arjeh M. Cohen and Jan Willem Knopper,
**Automatic proof of graph nonisomorphism**,*Mathematics in Computer Science***2**(2008) no. 2, 211-229. **Representations of parabolic and Borel subgroups**,*Communications in Algebra***35**(2007) no. 2, 455-459.

Additional material below.- With Arjeh M. Cohen and D. E. Taylor,
**Computing in groups of Lie type**,*Mathematics of Computation***73**(2004), 1477-1498. - With Arjeh Cohen, Martin Pollet and Volker Sorge,
**Certifying solutions to permutation group problems**,*Automated Deduction — CADE-19*, F. Baader (ed),*Lecture Notes in Artificial Intelligence***2741**(2003), 257-273.

Additional material below. - With Petra E. Holmes, Stephen A. Linton,
**Product replacement in the Monster group**,*Experimental Mathematics***12**(2003) no. 1, 123-126. - With C.R. Leedham-Green,
**Variants of product replacement**,*Computational and statistical Group Theory (Las Vegas, NV/Hoboken, NJ, 2001)*,*Contemporary Mathematics***298**(2002), 97-104. **Conjugacy classes in maximal parabolic subgroups of the general linear group**,*Journal of Algebra***233**(2000) no. 1, 135-155. arXiv:math/0001031

Additional material below.- With Frank Celler, C. R. Leedham-Green, Alice C. Niemeyer, and E. A. O’Brien,
**Generating random elements of a finite group**,*Communications in Algebra***23**(1995) no. 13, 4931-4948. - With E. A. O’Brien,
**Selecting base points for the Schreier-Sims algorithm for matrix groups**,*Journal of Symbolic Computation***19**(1995) no. 6, 577-584.

Additional material below.

## Other publications and work in progress

- With Lisa Carbone, Matt Kownacki, and Sowmya Srinivasan,
**Root subsystems of rank 2 hyperbolic root systems**, preprint. arxiv.org/1506.05405 - With Arjeh M. Cohen and Sergei Haller,
**Computing with root subgroups of twisted reductive groups**, preprint. - With Sophie Ambrose, Cheryl E. Praeger, Csaba Schneider,
**Constructive membership testing in black-box classical groups**, preprint. arXiv:1006.5858 - With Arjeh M. Cohen, Willem de Graaf, and D. E. Taylor,
**Coxeter groups**and**Lie groups**, chapters in*Handbook of Magma functions*, J. Cannon and W. Bosma eds., version 2.9 edition. - With Arjeh M. Cohen,
**An automated proof theory approach to computation with permutation groups**, course given by Arjeh Cohen at the Calculemus Autumn School 2002. - With Neil Saunders,
**Magma Proof of Strict Inequalities for Minimal Degrees of Finite Groups**, preprint. arXiv:0906.3574 - With Gene Cooperman,
**Computable subgroup chains and shadowing**, preprint. - With Arjeh M. Cohen,
**Constructive Sylow Theorems for exceptional groups of Lie type**, work in progress. - With Sergei Haller,
**Computing conjugacy in finite classical groups**, work in progress.

## Slides from selected presentations

**An application of Magma to groups acting on trees**, Invited plenary at Groups St Andrews 2009.**Computing with the Lie correspondence**, Invited talk at the Matrix Group Recognition meeting of the International Centre for Mathematical Sciences. I have also written a short note on applying Lang’s Theorem to groups of Lie type. This is based on a result in the book by Digne and Michel.**Overview of Lie theory in Magma**, Seminar at Rutgers University, March 2008.**Computing in groups of Lie type with Lie algebras**,*Magma workshop on group theory and algebraic geometry*, August 2005.**Computing in soluble linear algebraic groups**,*Groups St Andrews*, July 2005.**Using modular Lie algebras to compute with algebraic groups**,*Lie Algebras, their Classification and Applications*, Trento, July 2005.**Algorithm for Lang’s theorem**,*Victorian algebra conference*, Melbourne, September 2004.

## Projects by research students

This section contains successful PhD, Masters, and undergraduate projects by students I supervised or significantly assisted.

- Jan Willem Knopper,
**Automatic Proofs of Graph Nonisomorphism**, Undergraduate thesis, Technical University of Eindhoven, 2005. - Sergei Haller,
**Computing Galois cohomology and forms of linear algebraic groups**, PhD thesis, Technical University of Eindhoven, 2005. - Nguyen Van Minh Man,
**Computer-algebraic methods for the construction of designs of experiments**, PhD thesis, Technical University of Eindhoven, 2005. - Chris Krook,
**Groups related to***E*_{7}(*q*)**: A quest for distance-transitivity**, Masters thesis, Technical University of Eindhoven, 2003. - Vincent Remie,
**Graph isomorphism problem**, Undergraduate thesis, Technical University of Eindhoven, 2003.

## Theses, code, data, and appendices

Most of my code and data is included in the computer algebra systems Magma and/or GAP. This section provides links to code and other material that is available separately.

With Arjeh M. Cohen, **An algorithm for Lang’s Theorem**, *Journal of Algebra* **322 **(2009) no. 3, 675-702. arXiv:math/0506068

I have written a short note on applying Lang’s Theorem to groups of Lie type. This is based on results in: François Digne and Jean Michel,Representations of Finite Groups of Lie Type, Cambridge University Press(1991).

**Conjugacy classes in maximal parabolic subgroups of the general linear group**, *Journal of Algebra* **233 **(2000) no. 1, 135-155. arXiv:math/0001031

This paper is based on myPh.D. thesisof the same name. My advisor was Jon L. Alperin at the Department of Mathematics, University of Chicago.

With E. A. O’Brien, **Selecting base points for the Schreier-Sims algorithm for matrix groups**, *Journal of Symbolic Computation* **19 **(1995) no. 6, 577-584.

The implementation of the random Schreier-Sims algorithm used for this paper is also available.

This paper is based on part of my honours thesis calledThe Schreier-Sims algorithm. My supervisor was E. A. O’Brien at the School of Mathematical Sciences, Australian National University.

*With Arjeh M. Cohen, *** An automated proof theory approach to computation with permutation groups**, course given by Arjeh Cohen at the Calculemus Autumn School 2002.

The implementation in GAP of the methods discussed is available, along with some examples of its use.