# Neil Saunders

I am a Lecturer in Pure Mathematics at the University of Greenwich in the Department of Mathematical Sciences.

From October 2016 to September 2017, I was postdoctoral research fellow in the Department of Mathematics, Computer Science and Engineering at City University of London and from October 2015-September 2016 I was a postdoctoral researcher at the École Polytechinque Fédérale de Lausanne working in the Testerman Group on representations of algebraic groups. From October 2012-September 2015 I was a postdoctoral research fellow at the University of Bristol working in the Representation Theory Group. At this time I also co-organised the Algebra and Geometry Seminar as well as the 61st BLOC and 65th BLOC meetings in Bristol. I was also the Bristol representative to the London Mathematical Society.

# Research

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.

Recently I have started 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.

# Publications and Preprints

- Exotic Springer Fibres for Orbits Corresponding to one-row Biparitions (with A. Wilbert)
*In Preparation* - Irreducible Components of Exotic Springer Fibres II: The Robinson-Schensted Algorithm (with V. Nandakumar and D. Rosso) preprint 2017.
- Irreducible Components of Exotic Springer Fibres (with V. Nandakumar and D. Rosso) to appear in
*J. Lond. Math. Soc.* - Absorption of Direct Factors With Respect to the Minimal Faithful Permutation Degree of a Finite Group, (with D. Easdown and M. Hendriksen) submitted (2016)
- The Smallest Degree for a Direct Product Obeying an Inequality Condition, (with D. Easdown)
*Communications in Algebra*, 44, Issue 8, 3518-3537 (2016) - On Exceptional Groups of Order p^5, (with J.R. Britnell and T. Skyner)
*J. Pure Appl. Algebra*221, no. 11, 2647–2665 (2017) - Minimal Faithful Permutation Degrees for Irreducible Coxeter Groups and Binary Polyhedral Groups,
*J. Group Theory*, 17, No. 5, 805-832. MR3259095 (2014) - 10 is the Smallest Degree, Research Report for Aust-MS Lift-Off Fellowship, Australian Mathematical Society Gazette, 13, No. 5, 228-230. MR3060169 (2012)
- The minimal degree for a class of finite complex reflection groups,
*J. Algebra*, 323, 561–573. MR2574852 (2010) - Strict inequalities for minimal degrees of direct products, Bulletin of the Australian Mathematical Society, 79, no. 1, 23–30. MR2486877 (2009)
- 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
- Magma Proof of Strict Inequalities for Minimal Degrees of Finite Groups(with S.H. Murray) 2009
- Minimal Faithful Permutation Degrees of Finite Groups, Australian Mathematical Society Gazette,35 (2008), No. 2, 332–338. MR2473204