Dr Simon Goodwin PhD, MMath

Dr Simon Goodwin

School of Mathematics
Senior Lecturer

Contact details

School of Mathematics
University of Birmingham
B15 2TT

Simon Goodwin is a Senior Lecturer in pure mathematics in the School of Mathematics.  His research interests are in representation theory and Lie theory.

School web page: web.mat.bham.ac.uk/S.M.Goodwin


  • 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 a Senior Lecturer.


  • 1ACa Algebra 1
  • 2ACa 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.

PhD opportunities


Representation theory and Lie theory:

  • algebraic groups
  • Lie algebras
  • W-algebras
  • finite group of Lie type


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 superalgebra, 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. He also works in problems in the related to the representation theory of finite groups of Lie type and their structure.

Please see my publications for more information.



Goodwin, S. M., Le, T., Magaard, K., Paolini, A. (2016), Constructing characters of Sylow p-subgroups of finite Chevalley groups. Journal of Algebra 468 (2016), 395–439.

Goodwin, S. M, Mosch, P., Röhrle, G. (2016), On the coadjoint orbits of maximal unipotent subgroups of reductive groups.,Transformation Groups 21 (2016), 399–426. 


Brown, J. S, Brundan, J. (2013),  Goodwin, S. M., Principal W-algebras for GL(m|n), Algebra Number Theory 7 (2013), no. 8, 1849–1882.

Brown, J. S, Goodwin, S. M. (2013), Finite dimensional irreducible representations of finite W-algebras associated to even multiplicity nilpotent orbits in classical Lie algebras. Mathematische Zeitschrift 273 (2013),  123–160.

Goodwin, S. M. (2011), Translation for finite W-algebras, Representation Theory 15 (2011), 307–346.

Goodwin, S. M., Röhrle, G. (2009), Rational points on generalized flag varieties and unipotent conjugacy in finite groups of Lie type, Transactions of the American Mathematical Society 361 (2009), 177–206.

Brundan, J., Goodwin, S. M. and A Kleshchev, A. (2008), Highest weight theory for finite W-algebras, International Mathematics Research Notices (2008) Vol. 2008: article ID rnn051.

Brundan, J. and Goodwin, S. M. (2007), Good grading polytopes, Proceeding of the London Mathematical Society (3) 94 (2007), 155–180.

Goodwin, S. M. (2006), On the conjugacy classes in maximal unipotent subgroups of simple algebraic groups, Transformation Groups 11 (2006), 51–76.