The beauty of symmetry

Full article issued by The University of Western Australia.

Emeritus Professor Cheryl Praeger AC FAA is a multiple award-winning professor and multiple ARC grant recipient with a passion for mathematics. Her work is complex with key research in the field of group theory, particularly permutation groups and combinatorics, a branch of pure mathematics which studies symmetry. Part of the internationally-recognised team of pure mathematicians at the Mathematics of Symmetry and Computation Research Cluster at The University of Western Australia (UWA), Professor Praeger's work has been influential in many academic and real-world applications.

Professor Praeger has long been interested in symmetry, and in 1979, a new mega theorem called 'Finite Simple Group Classification' identified the mathematical building blocks of symmetry. The theory spanned across algebra and combinatorics and changed the problems that could be solved and the methods used to solve them, and paved the way for Professor Praeger to make several breakthroughs by applying the classification to group theory and permutation groups.

In recent work, supported by an ARC Discovery Projects grant, Professor Praeger's team has studied how 'homogeneous' (in some sense, how 'symmetric') the finite simple groups can be. They introduce a parameter which measures the homogeneity, and have been able to prove that the largest of the sporadic simple groups – dubbed the 'Monster' – is uniquely the most homogeneous simple group. It is speculated that the Monster might be associated with quantum gravity and might even be the symmetry group of a black hole.

Professor Praeger started at UWA in 1976. She was appointed Professor in 1983 at age 35, whilst a mother of two pre-school children, and only the second woman professor of mathematics at an Australian university. Awarded the Australian Academy of Science's 2021 Inaugural Ruby Payne-Scott Medal and Lecture, as well as the 2019 Prime Minister’s Prize for Science for her extensive service, and in particular for her fundamental work in group theory and combinatorics, Professor Praeger is a role model for women in mathematics, and an inspiring story of impactful and groundbreaking research discovery.

 

 

Professor Cheryl Praeger, an internationally respected mathematician. Image Credit: UWA.