Publications
Research publications by members of the Computational Algebra Group at the University of Sydney, spanning 2026 to 1988.
2026
Computing Class Groups and Unit Groups in Magma
Proceedings of the 2026 International Symposium on Symbolic and Algebraic Computation
The constructive inverse Galois problem via Hilbert modular forms: realizing the transitive group 17T7
arXiv
Explicit modularity of K3 surfaces with complex multiplication of large degree
LuCaNT: Databases, Algorithms, and Computational Number Theory, Contemporary Mathematics
A framework for Tate modules of abelian varieties under isogeny
Essential Number Theory
Hypergeometric motives from Euler integral representations
Journal of the London Mathematical Society
Constructing ordinary representations of finite groups via extension
Journal of Algebra
QRT map on a bielliptic surface
Journal of Physics A: Mathematical and Theoretical
Influence of the geometry on the mechanical performance of tubular interlockings: A study of the Sine Block
JOURNAL OF SOLIDS AND STRUCTURES
Construction of Toroidal Polyhedra corresponding to perfect Chains of isosceles Tetrahedra
Journal of Geometry
Topologically Interlocking Blocks Inside the Tetroctahedrille
Nexus Network Journal
A census of Cayley graphs
Journal of Symbolic Computation
2025
On abelian varieties whose torsion is not self-dual
Proceedings of the American Mathematical Society Series B
Computing class groups and unit groups in Magma
arXiv
Explicit modularity of K3 surfaces with complex multiplication of large degree
arXiv
Computing Hilbert modular forms as orthogonal modular forms
arXiv
On Galois inertial types of elliptic curves over Q_{p}
Mathematics of Computation, American Mathematical Society (AMS)
Simplicial surfaces with given automorphism group
Journal of Algebraic Combinatorics
Tightness of the Weight‐Distribution Bound for Strongly Regular Polar Graphs
Journal of Combinatorial Designs
Equitable 2-partitions of the Johnson graphs J(n,3)
Discrete Mathematics
Computing quadratic subfields of number fields
J. Comput. Algebra
2024
GROUPS WITH FEW NONPOWER SUBGROUPS
Bulletin of the Australian Mathematical Society
Ideal classes of orders in quaternion algebras
Journal of Pure and Applied Algebra228(7):107649Elsevier
A database of basic numerical invariants of Hilbert modular surfaces
LuCaNT: LMFDB, Computation, and Number Theory, Contemporary Mathematics
A database of paramodular forms from quinary orthogonal modular forms
LuCaNT: LMFDB, Computation, and Number Theory, Contemporary Mathematics
Hurwitz's lectures on the number theory of quaternions
European Mathematical Society Magazine
Rational torsion points on abelian surfaces with quaternionic multiplication
Forum of Mathematics Sigma
Bianchi period polynomials: Hecke action and congruences
Research in Number Theory
Minimization of hypersurfaces
Math. Comp.
Real and complex multiplication on K3 surfaces via period integration
Exp. Math.
On the component group of the algebraic monodromy group of a K3 surface
J. Algebra
Computing Galois groups
Int. J. Group Theory
2023
Explicit families of K3 surfaces having real multiplication
Michigan Math. J.
Computing splitting fields using Galois theory and other Galois constructions
Journal of Symbolic Computation
2022
Frobenius trace distributions for K3 surfaces
J. Ramanujan Math. Soc.
2-adic point counting on K3 surfaces
Res. Number Theory
2021
Most permutations power to a cycle of small prime length
Proceedings of the Edinburgh Mathematical Society
Galois groups over rational function fields and Explicit Hilbert Irreducibility
Journal of Symbolic Computation
2020
The Hasse norm principle in global function fields
Women in Numbers Europe III: Research Directions in Number Theory. Papers from the Workshop (WIN-E3) held at La Hublais, Cesson-Sévigné (France)
Constructions using Galois Theory
ArXiv
Construction of the irreducible modular representations of a finite group
Journal of Algebra
Computing invariants of cubic surfaces
Matematiche (Catania)
2019
Almost all permutations power to a cycle of prime length
arXiv
Existence results for primitive elements in cubic and quartic extensions of a finite field
Math. Comp.
An algorithm for computing Schur indices of characters
Journal of Symbolic Computation
Primitive values of quadratic polynomials in a finite field
Mathematics of Computation
Computing subfields of number fields and applications to Galois group computations
Journal of Symbolic Computation
Class number one from analytic rank two
Mathematika
Fast detection of giant permutation groups
Computing the socle of a large permutation group
Plane quartics with a Galois-invariant Steiner hexad
Int. J. Number Theory
The use of permutation representations in structural computations in large finite matrix groups
Journal of Symbolic Computation
On plane quartics with a Galois invariant Cayley octad
Eur. J. Math.
2018
Normalisers of parabolic subgroups in finite unitary reflection groups
Journal of Algebra
Jacobi sums and Grössencharacters
Publications math'ematiques de Besançon
2017
Losing Chess: 1. E3 Wins for White
ICGA Journal
2016
Point counting on K3 surfaces and an application concerning real and complex multiplication
LMS J. Comput. Math., suppl. A
An application of the p-adic analytic class number formula
LMS Journal of Computation and Mathematics
Groups equal to a product of three conjugate subgroups
Israel Journal of Mathematics
Algorithms for Galois Extensions of Global Function Fields
Bulletin of the Australian Mathematical Society
On the local-global principle for divisibility in the cohomology of elliptic curves
Mathematical Research Letters
2015
Proceedings of the 7th International Workshop on Parallel Symbolic Computation
Appendix to Denominators of algebraic numbers in a number field by M. Ayad, A. Bayad and O. Kihel
J. Num. Thy
Moduli spaces and the inverse Galois problem for cubic surfaces
Transactions of the AMS
Two torsion in the Brauer group of a hyperelliptic curve
Manuscripta Math.
On the characteristic polynomial of the Frobenius on 'etale cohomology
Duke Mathematical Journal
2014
Subexponential class group and unit group computation in large degree number fields.
LMS Journal of Computation and Mathematics [electronic only ]
Computing in quotients of rings of integers.
LMS Journal of Computation and Mathematics [electronic only ]
Computation of Galois groups of rational polynomials.
LMS Journal of Computation and Mathematics [electronic only ]
Second p-descents on elliptic curves
Mathematics of Computation
Solved openings in Losing Chess
ICGA Journal
2013
Locally trivial torsors that are not Weil-Châtelet divisible
Bulletin of the London Mathematical Society
Some Comments about Indefinite LLL
Diophantine Methods, Lattics, and Arithmetic Theory of Quadratic Forms, Proceedings of a BIRS Workshop
$p$-adic verification of class number computations
Explicit descent in the Picard group of a cyclic cover of the projective line
ANTS X: Proceedings of the Tenth Algorithmic Number Theory Symposium
Explicit Methods in Number Theory
2012
A Grunwald-Wang type theorem for abelian varieties
Acta Arith.
An extension of Kedlaya's algorithm for hyperelliptic curves
J. Symbolic Computation
Algorithms for Del Pezzo Surfaces of Degree 5 (Construction, Parametrization)
J. Symbolic Computation
Minkowski polynomials and mutations
SIGMA Symmetry Integrability Geom. Methods Appl.
Some remarks on Heegner point computations
Explicit Methods in Number Theory
Another 80-dimensional extremal lattice
Journal de th'eorie des nombres de Bordeaux
2011
Potential Sha for abelian varieties
Journal of Number Theory
The great trinomial hunt
Notices of the American Mathematical Society
On the Equivalence of Quadratic APN Functions
Designs, Codes and Cryptography
Unifying some known infinite families of combinatorial 3-designs
J. Comb. Theory, Ser. A
On the computation of local components of a newform
Mathematics of Computation
Constructive homomorphisms for classical groups
Journal of Symbolic Computation
Proving finitely presented groups are large by computer
Experiment. Math.
Secant varieties to Lagrangian Grassmannians
Annali di Mat Pura ed Applicata
An LLL-Reduction algorithm with quasi-linear time complexity
Proc. 43rd ACM Symposium on Theory of Computing
Rank 7 quadratic twist(s) of the congruent number curve
Explicit Methods in Number Theory
A new automorphism of X0(108)
Some Comments about Indefinite LLL
Diophantine Methods, Lattics, and Arithmetic Theory of Quadratic Forms
2010
Nondegenerate curves of low genus over small finite fields
Arithmetic, Geometry, Cryptography and Coding Theory 2009
An O(M(n) log n) algorithm for the Jacobi symbol
Algorithmic Number Theory (Ninth International Symposium, ANTS-IX)
Modern Computer Arithmetic
Accelerating lattice reduction with FPGAs
Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
On the Birch-Swinnerton-Dyer quotients modulo squares
Annals of Math.
On Coxeter's families of group presentations
J. Algebra
Constructing maximal subgroups of orthogonal groups
LMS J. Comput. Math.
Faster Fully Homomorphic Encryption
Advances in Cryptology - ASIACRYPT 2010
2009
Finite Weil-representations and associated Hecke-algebras
J. Number Theory
Solving the Shortest Lattice Vector Problem in Time 2^2.465n
Unitary reflection groups
On the extremality of an 80-dimensional lattice
Explicit Methods in Number Theory
2008
Embeddings of complex line systems and finite reflection groups
J. Aust. Math. Soc.
2007
Some long-period random number generators using shifts and xors
ANZIAM Journal
Geometric automorphism groups of graphs
Discrete Appl. Math.
2002
2001
Matrix generators for exceptional groups of Lie type
J. Symbolic Comput.
Two results concerning distance-regular directed graphs
Australas. J. Combin.
2000
Constructions for octonion and exceptional Jordan algebras
Des. Codes Cryptogr.
1999
1998
Matrix generators for the orthogonal groups
J. Symbolic Comput.
1997
On outer automorphism groups of Coxeter groups
Manuscripta Math.
1994
Vertex-primitive half-transitive graphs
J. Austral. Math. Soc. Ser. A
1992
Introductory lectures on Siegel modular forms (Book Review)
The geometry of the classical groups
A decomposition of the descent algebra of a finite Coxeter group
J. Algebraic Combin.
1988
Polynomial-time versions of Sylow's theorem
J. Algorithms