Dane Flannery

Personal Professor in Mathematics
School of Mathematical and Statistical Sciences, University of Galway, Ireland
E-mail: dane.flannery@universityofgalway.ie

Linear (matrix) groups

• Zariski density and computing with S-integral groups

• Freeness and S-arithmeticity of rational Möbius groups

• Classifying finite monomial groups in characteristic zero and any prime degree; an implementation

• Experimenting with symplectic monodromy groups

• Strong approximation and computing with linear groups

• Long survey on linear groups and computation  (2018; outdated)

• Practical algorithms for Zariski dense subgroups

• Oberwolfach preprints 1, 2, 3, 4

• Zariski density and computing in arithmetic groups

• L. G. Kovács and linear groups

• Algorithms for arithmetic groups with the congruence subgroup property

• Arithmeticity and integrality of solvable linear groups

• Computing with linear groups of finite rank

• Recognizing finite matrix groups

• Deciding virtual properties of linear groups

• Short survey on computing with matrix groups over infinite fields (2009)

• Early steps in computing with matrix groups over infinite fields 1, 2, 3

• Nilpotent and locally nilpotent linear groups 1, 2

• More classifications of linear groups 1, 2, 3, 4, 5

• Magma chapter on computing with matrix groups over infinite fields

• The GAP package Nilmat

Algebraic design theory

• Book co-authored with Warwick de Launey

• Special Issue on Design Theory

• On quasi-orthogonal cocycles

• Generalized binary arrays from quasi-orthogonal cocycles

• Almost supplementary difference sets and optimal quaternary sequences

• Quasi-orthogonal cocycles, optimal sequences, and a conjecture of Littlewood's

• Generalized partially bent functions, generalized perfect arrays and cocyclic Butson matrices

• Automorphisms of generalized Sylvester Hadamard matrices

• On linear shift representations

• Classifying cocyclic Butson Hadamard matrices

Miscellanea

• Probabilistic group theory, combinatorics, and computing

• • A snapshot

  • Public lecture by Efim Zelmanov

  • Advice

Conferences

• 6th Workshop on Algebraic Designs, Hadamard Matrices & Quanta Kraków, June 27–July 2, 2022. Video

• Computational Aspects of Discrete Subgroups of Lie Groups ICERM, June 14–18, 2021

• Computational and algorithmic methods Isaac Newton Institute for Mathematical Sciences, Cambridge, January 27–31, 2020

• Fifth de Brún Workshop

• Third de Brún Workshop on Computational Algebra

• International Conference on Design Theory and Applications

Funding

• PI of three Science Foundation Ireland Research Frontiers Programme awards: 11/RFP/MTH3212, 08/RFP/MTH1331, and RFP05/MAT0008

• Co-PI of a Science Foundation Ireland Mathematics Initiative 2007 award, 07/MI/007

• PI of two Irish Research Council New Foundations awards (A new foundation for matrix group algorithms, 2014; Matrix groups: algorithms and applications, 2015)

Doctoral and Masters students

• Dr Tobias Rossmann (PhD 2011, co-supervised with Dr Alla Detinko)

• Dr Padraig Ó Catháin (MLitt 2008, PhD 2012)

• Dr Ronan Egan (PhD 2015)

In memoriam Laci Kovács, Warwick de Launey