Neil Saunders 

My PhD research focused on the problem of minimally embedding finite groups in symmetric groups. This is a long standing problem of interest to group theorists and algebraists alike and has interesting theoretical and computational consequences. More specifically, the minimal faithful permutation degree of a finite group is the smallest non-negative integer for which the group embeds inside symmetric group. This defines an invariant for the finite group. My PhD thesis investigated how this invariant behaves under familiar group theory constructions such as direct product and homomorphic image.

Since my PhD, I have been working on areas related to geometric representations of algebraic groups. Specifically, I have become interested in topics related to the Springer Correspondence. The so-called Springer Fibres lie at the heart of this and have some rich geometrical features, and the irreducible components of these fibres often admit tractable combinatorial and diagrammatic descriptions.

Up until August 2012, I was an Associate Lecturer in the School of Mathematics and Statistics at the University of Sydney, where I also completed my PhD in late 2010. My supervisor was Associate Professor David Easdown and my associate supervisor was Associate Professor Anthony Henderson.

In December 2010, I was awarded a Lift-Off Fellowship by the Australian Mathematical Society, of which only five are awarded annually to recently submitted PhD students. In October 2008, I was awarded the G.B. Preston Prize for the best student talk at the 26th Victorian Algebra Conference held at RMIT University, Melbourne. In September 2007, I was jointly awarded the B.H. Neumann Prize for the best talk given by a student at the 51st Annual Meeting of the Australian Mathematical Society held at La Trobe University.

1. Parabolic Induction for Springer Fibres (with L. Topley), Proceedings of the American Mathematical Society, 151 (8): 3331-3345  (2023)

2. Irreducible Components of Exotic Springer Fibres II: The Robinson-Schensted Algorithm (with V. Nandakumar and D. Rosso) Pacific Journal of Mathematics, 310 (2), 447-485 (2021)

3. Exotic Springer Fibres for Orbits Corresponding to one-row Biparitions (with A. Wilbert) to appear in Transformation Groups, 1-37 (2020)

4. Irreducible Components of Exotic Springer Fibres (with V. Nandakumar and D. Rosso) J. Lond. Math. Soc. 98 (3): 609-637 (2018) doi:10.1112/jlms.12152

5. Absorption of Direct Factors With Respect to the Minimal Faithful Permutation Degree of a Finite Group, (with D. Easdown and M. Hendriksen) submitted (2016)

6. The Smallest Degree for a Direct Product Obeying an Inequality Condition, (with D. Easdown) Communications in Algebra, 44, Issue 8, 3518-3537 (2016)

7. On Exceptional Groups of Order p^5, (with J.R. Britnell and T. Skyner)  J. Pure Appl. Algebra 221, no. 11, 2647–2665  (2017)

8. Minimal Faithful Permutation Degrees for Irreducible Coxeter Groups and Binary Polyhedral Groups, J. Group Theory, 17, No. 5, 805-832. MR3259095 (2014)

9. 10 is the Smallest Degree, Research Report for Aust-MS Lift-Off Fellowship, Australian Mathematical Society Gazette, 13, No. 5, 228-230. MR3060169 (2012)

10. The minimal degree for a class of finite complex reflection groups, J. Algebra, 323, 561–573. MR2574852 (2010)

11. Strict inequalities for minimal degrees of direct products, Bulletin of the Australian Mathematical Society, 79, no. 1, 23–30. MR2486877 (2009)

12. Learning and teaching in summer: is it better and why?, Motivating Science Undergraduates: Ideas and Interventions, Motivating Science Undergraduates: Ideas and Interventions, Alexandra Hugman (ed.), UniServe Science Conference Proceedings, UniServe Science, The University of Sydney, (2009), 24–29. ISBN 978-1-74210-149-1, Co- authored with Easdown D, Ancev T, Bishop T, Mansfield S, Ougrinovskaia A, Warren D

13. Magma Proof of Strict Inequalities for Minimal Degrees of Finite Groups(with S.H. Murray) 2009 

14. Minimal Faithful Permutation Degrees of Finite Groups, Australian Mathematical Society Gazette,35 (2008), No. 2, 332–338. MR2473204

1. Maths degrees are becoming less accessible – and this is a problem for business, government and innovation, published in The Conversation UK, May 2024. Also published in Phys.org

2. A review of Kit Yates' How to Expect The Unexpected - The Science of Making Predictions and the Art of Knowing When Not To in LMS Newletter, Issue 510 February 2024, pg 36-37

3. Rishi Sunak wants more maths at school – but finding the teachers will be hard when university departments are closing, originally published in The Conversation UK, December 2023. Also published in The Irish News, The Quint (India)

4. Evolution is making us treat AI like a human, and we need to kick the habit, originally published in The Conversation UK, May 2023. Also published in Metro UK, TheWire.in, The Businnes Stantard (India), SiliconRepublic, Rationale Magazine, CAPX, AsiaTimes, EconoTimes

5. AI is staggeringly competent, but it doesn't comprehend a thing  - as google's Lamda shows, published in Medium, June 2022

6. A review of Kit Yates' The Maths of Life and Death — why maths is (almost) everything in LMS Newsletter, May 2020, pg 41-42