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About Tomasz
Tomasz Popiel is a Lecturer in the School of Mathematics at Monash University in the Faculty of Science. He earned his PhD in 2007 from the University of Western Australia, with a dissertation entitled 'Geometrically-Defined Curves in Riemannian Manifolds' supervised by J. Lyle Noakes. Before joining Monash, Popiel held a temporary lecturer position in pure mathematics at the University of Canterbury in 2021. He was appointed Lecturer in Algebra at Monash University in 2023. His research spans finite group theory, discrete structures—particularly finite incidence geometries—and the actions of finite groups on these structures. He also investigates purely group-theoretic problems related to finite simple groups, including aspects of their representation theory, building on his PhD work in differential geometry.
Popiel's publications reflect his diverse interests and collaborations with prominent mathematicians. Early works include 'Bézier curves and interpolation in Riemannian manifolds' (Journal of Approximation Theory, 2007, 102 citations), 'Spherical Bézier splines' (Computer Aided Geometric Design, 2006, 39 citations), 'Geometry for robot path planning' (Robotica, 2007, 30 citations), and 'Quadratures and cubics in SO(3) and SO(1,2)' (IMA Journal of Mathematical Control and Information, 2006, 27 citations). Recent contributions focus on computational group theory and sporadic simple groups, such as 'The maximal subgroups of the Monster' (Advances in Mathematics, 2025, with Heiko Dietrich and Melissa Lee, 25 citations), 'Conjugacy class fusion from four maximal subgroups of the Monster' (with Anthony Pisani), 'Derangements in permutation groups with two orbits' (Bulletin of the Australian Mathematical Society, 2026, with Melissa Lee and Gabriel Verret), 'Generalized quadrangles and transitive pseudo-hyperovals' (Journal of Combinatorial Designs, 2016, with John Bamberg, Simon P. Glasby, and Cheryl E. Praeger, 16 citations), and 'Saxl graphs of primitive affine groups with sporadic point stabilizers' (International Journal of Algebra and Computation, 2023). With over 490 citations on Google Scholar, his research has impacted areas like combinatorial geometry and group recognition. At Monash, he coordinates the unit MTH2019: Multivariate mathematics for data science.
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