Dr Simon Goodwin PhD, MMath

Dr Simon Goodwin

School of Mathematics
Reader in Pure Mathematics

Contact details

School of Mathematics
University of Birmingham
B15 2TT

Simon Goodwin is Reader in Pure Mathematics in the School of Mathematics.  His research interests are in representation theory and Lie theory.  Simon's recent research has focussed on representation theory of modular lie algebras and finite W-algebras, and 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 Reader in Pure Mathematics.


Simon enjoys teaching the first and second year algebra courses 1AC Algebra 1 and 2AC Algebra 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.


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. https://doi.org/10.1007/s00031-022-09722-y

Goodwin, S & Topley, L 2021, 'Restricted shifted Yangians and restricted finite W-algebras', Transactions of the American Mathematical Society, vol. 8, pp. 190–228. https://doi.org/10.1090/btran/63

Goodwin, S & Topley, L 2019, 'Minimal dimensional representations of reduced enveloping algebras for gln', Compositio Mathematica, vol. 155, no. 8, pp. 1594-1617. https://doi.org/10.1112/S0010437X19007474

Goodwin, SM & Topley, LW 2019, 'Modular finite W-algebras', International Mathematics Research Notices, vol. 2019, no. 18, pp. 5811–5853. https://doi.org/10.1093/imrn/rnx295

Brundan, J & Goodwin, S 2019, 'Whittaker coinvariants for GL(m|n)', Advances in Mathematics, vol. 347, pp. 273-339. https://doi.org/10.1016/j.aim.2019.02.025

Goodwin, S & Brown, J 2018, 'On the variety of 1-dimensional representations of finite W-algebras in low rank', Journal of Algebra. https://doi.org/10.1016/j.jalgebra.2018.03.030

Goodwin, S, Mosch, P & Roehrle, G 2018, 'The Modality of a Borel Subgroup in a Simple Algebraic Group of Type E8', Experimental Mathematics. https://doi.org/10.1080/10586458.2018.1468289

Goodwin, S & Goddard, R 2017, 'On commuting varieties of parabolic subalgebras', Journal of Pure and Applied Algebra. https://doi.org/10.1016/j.jpaa.2017.04.015

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. https://doi.org/10.1080/00927872.2017.1298771

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. https://doi.org/10.1016/j.jalgebra.2016.06.039

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. https://doi.org/10.1017/S0013091513000746

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. https://doi.org/10.1007/s00031-015-9318-9

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. https://doi.org/10.1112/S1461157013000284

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. https://doi.org/10.1080/00927872.2013.777845

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. https://doi.org/10.2140/pjm.2014.269.31

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