Professor Simon Goodwin MMath PhD

Professor Simon Goodwin

School of Mathematics
Professor of Pure Mathematics

Contact details

School of Mathematics
Watson Buliding
University of Birmingham
B15 2TT

Simon Goodwin is Professor of Pure Mathematics in the School of Mathematics. His research interests are in representation theory and Lie theory. His recent research on representation theory of modular Lie algebras and finite W-algebras is supported by EPSRC funding.


  • PhD Mathematics, University of Birmingham, 2005
  • MMath Mathematics, University of Oxford, 2001


Simon Goodwin completed his MMath degree at the University of Oxford in 2001. He studied for his PhD at the University of Birmingham, which was completed in 2004. After his PhD he took a one year postdoctoral research position at the University of Aarhus, before taking up a Junior Research Fellowship at the University of Oxford. Simon returned to the University of Birmingham in 2006, when he was appointed as a Birmingham Research Fellow, and is now Professor of Pure Mathematics.


Semester 1

LC/LI Algebra and Combinatorics 1

Semester 2

LI/LH Algebra and Combinatorics 2

Postgraduate supervision

Simon supervises PhD and MRes projects on a range of different topics related to the representation theory and structure theory of algebraic groups and Lie algebras, and is interested in supervising new students.


Research Activity

Simon's research interests cover a range of topics in representation theory and Lie theory. His interests are centered around questions in the representation theory of Lie algebras and algebraic groups. Recently he has been interested in the representation theory of modular Lie algebras and of Lie superalgebras, and in particular the application of the theory of W-algebras to these areas. This research has involved a blend of algebraic, combinatorial and geometric methods, and is supported by EPSRC funding.


Recent publications


Goodwin, SM & Pengelly, R 2022, 'On 𝔰𝔩2-triples for classical algebraic groups in positive characteristic', Transformation Groups.

Goodwin, S & Topley, L 2021, 'Restricted shifted Yangians and restricted finite W-algebras', Transactions of the American Mathematical Society, vol. 8, pp. 190–228.

Goodwin, S & Topley, L 2019, 'Minimal dimensional representations of reduced enveloping algebras for gln', Compositio Mathematica, vol. 155, no. 8, pp. 1594-1617.

Goodwin, SM & Topley, LW 2019, 'Modular finite W-algebras', International Mathematics Research Notices, vol. 2019, no. 18, pp. 5811–5853.

Brundan, J & Goodwin, S 2019, 'Whittaker coinvariants for GL(m|n)', Advances in Mathematics, vol. 347, pp. 273-339.

Goodwin, S & Brown, J 2018, 'On the variety of 1-dimensional representations of finite W-algebras in low rank', Journal of Algebra.

Goodwin, S, Mosch, P & Roehrle, G 2018, 'The Modality of a Borel Subgroup in a Simple Algebraic Group of Type E8', Experimental Mathematics.

Goodwin, S & Goddard, R 2017, 'On commuting varieties of parabolic subalgebras', Journal of Pure and Applied Algebra.

Magaard, K, Goodwin, S & Le, T 2017, 'The generic character table of a Sylow $p$-subgroup of a finite Chevalley group of type $D_4$', Communications in Algebra.

Goodwin, SM, Le, T, Magaard, K & Paolini, A 2016, 'Constructing characters of Sylow p-subgroups of finite Chevalley groups', Journal of Algebra, vol. 468, pp. 395–439.

Goodwin, SM & Röhrle, G 2015, 'On Commuting Varieties of Nilradicals of Borel Subalgebras of Reductive Lie Algebras', Edinburgh Mathematical Society. Proceedings, vol. 58, no. 01, pp. 169-181.

Goodwin, SM, Mosch, P & Roehrle, G 2015, 'On the coadjoint orbits of maximal unipotent subgroups of reductive groups', Transformation Groups, vol. 21, no. 2, pp. 399-426.

Goodwin, SM, Mosch, P & Röhrle, G 2014, 'Calculating conjugacy classes in Sylow -subgroups of finite Chevalley groups of rank six and seven', London Mathematical Society. Journal of Computation and Mathematics, vol. 17, no. 01, pp. 109-122.

Bradley, JD & Goodwin, SM 2014, 'Conjugacy Classes in Sylow p-Subgroups of Finite Chevalley Groups in Bad Characteristic', Communications in Algebra, vol. 42, no. 8, pp. 3245-3258.

Brown, J & Goodwin, SM 2014, 'Representation theory of type B and C standard Levi W-algebras', Pacific Journal of Mathematics, vol. 269, no. 1, pp. 31-71.

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