Neil Saunders

Dr Neil Saunders

Senior Lecturer in Mathematical Sciences

Neil works in the field of algebra, specifically group theory and geometric representation theory. His PhD was in the theory of finite groups: the specific problem being finding the smallest degree symmetric group that an arbitrarily given finite group embeds in; and how this invariant behaves under group theoretic constructions. This is a classical problem in finite group theory having both computational and theoretical consequences.

In recent years, Neil’s research has focused on geometric and combinatorial aspects of representation theory. His work here has revolved around the Springer Correspondence, which provides a bijection between geometric data of an algebraic group acting on its nilpotent cone and the irreducible representations of the Weyl group of that algebraic group. Some consequences of this correspondence are that one may catalogue irreducible components of Springer fibres by means of (bi)tableaux and explicitly describe their geometry. This has applications in combinatorial representation theory and diagrammatic algebra.

Mathematics

Computer science and informatics

Responsibilities within the university

Course Leader 2019-2020

MATH1148 Foundations in Mathematics A

MATH1167 Techniques of Calculus and Linear Algebra

MATH1135 Graph Theory and Applications

Awards
  • Shortlisted for a Student Led Teaching Award 2019
  • Focused Research Week, £7000, Heilbronn Institute for Mathematical Research, 2019
  • Celebrating New Appointments, £573 London Mathematical Society, Scheme 9, 2018
  • Lift-Off Fellowship $4500 AUD from the Australian Mathematical Society, 2011
  • Dean's Award for Citizenship, Faculty of Science, University of Sydney, 2009
  • B.H. Neumann Prize for the Best Student Talk, Meeting of the AustMS 2007
  • G.B Preston Prize for the Best Student Talk, Victorian Algebra Conference, 2006 & 2008

Recognition

Fellow of the Higher Education Academy

Member of the London Mathematical Society

Member of the Australian Mathematical Society

Research / Scholarly interests

Neil works in the field of algebra, specifically group theory and geometric representation theory. His PhD was in the theory of finite groups: the specific problem being finding the smallest degree symmetric group that an arbitrarily given finite group embeds in; and how this invariant behaves under group theoretic constructions. This is a classical problem in finite group theory having both computational and theoretical consequences.

In recent years, Neil’s research has focused on geometric and combinatorial aspects of representation theory. His work here has revolved around the Springer Correspondence, which provides a bijection between geometric data of an algebraic group acting on its nilpotent cone and the irreducible representations of the Weyl group of that algebraic group. Some consequences of this correspondence are that one may catalogue irreducible components of Springer fibres by means of (bi)tableaux and explicitly describe their geometry. This has applications in combinatorial representation theory and diagrammatic algebra.

Key funded projects

  • May 2020 | London Math. Soc. Scheme 4: Research in Pairs
    £1000 - University of Greenwich (jointly awarded with Dr Daniele Rosso)
  • Aug 2019 | Heilbronn Focused Research Workshop: Springer Fibres and Geometric Representation Theory
    £7000 - University of Greenwich
  • Apr 2019 | London Math. Soc. Scheme 9: Celebrating New Appointments
    £575 - University of Greenwich
  • Jul 2016 | Representations of Algebra Groups: A conference in honour of Professor Stephen Donkin’s 60th Birthday £8500 (London Math. Soc. - £6000, Heilbronn Institute - £2500)
  • Jan 2011 | Lift-Off Fellowship
    $5000 AUD - Australian Mathematical Society

Recent publications

Article

Saunders, Neil and , Topley, Lewis (2022), Parabolic induction for springer fibres. American Mathematical Society. In: , , , . American Mathematical Society, Proceedings of the American Mathematical Society ISSN: 0002-9939 (Print), 1088-6826 (Online) (doi: ).

Nandakumar, Vinoth , Rosso, Daniele, Saunders, Neil (2021), Irreducible components of exotic Springer fibres II: The Exotic Robinson-Schensted algorithm. Mathematical Sciences Publishers (MSP). In: , , , . Mathematical Sciences Publishers (MSP), Pacific Journal of Mathematics Pacific Journal of Mathematics, 310 (2) . pp. 447-485 ISSN: 0030-8730 (Print), 1945-5844 (Online) (doi: https://doi.org/10.2140/pjm.2021.310.447).

Nandakumar, Vinoth , Rosso, Daniele, Saunders, Neil (2018), Irreducible components of exotic Springer fibres. Wiley. In: , , , . Wiley, Journal of the London Mathematical Society, 98 (3) . pp. 609-637 ISSN: 0024-6107 (Print), 1469-7750 (Online) (doi: https://doi.org/10.1112/jlms.12152).

Britnell, John R. , Saunders, Neil, Skyner, Tony (2016), On exceptional groups of order p⁵. Elsevier. In: , , , . Elsevier, Journal of Pure and Applied Algebra, 221 (11) . pp. 2647-2665 ISSN: 0022-4049 (Print), (doi: https://doi.org/10.1016/j.jpaa.2016.12.009).

Easdown, David and , Saunders, Neil (2016), The minimal faithful permutation degree for a direct product obeying an inequality condition. Taylor & Francis. In: , , , . Taylor & Francis, Communications in Algebra, 44 (8) . pp. 3518-3537 ISSN: 0092-7872 (Print), 1532-4125 (Online) (doi: https://doi.org/10.1080/00927872.2015.1085548).

Working paper

Saunders, Neil and , Wilbert, Arik (2020), Exotic Springer fibers for orbits corresponding to one-row bipartitions. Transformation Groups. In: , , , . Transformation Groups, (doi: ) NB Item availability restricted.

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