Dr Adam Thomas PhD, MMath

Dr Adam Thomas

School of Mathematics
Research Fellow in Representation Theory

Contact details

Address
University of Birmingham
Edgbaston
Birmingham
B15 2TT
UK

Adam Thomas is a Research Fellow in Representation Theory in the School of Mathematics. His research interests are mainly algebraic including group theory, Lie algebras and representation theory.

Qualifications

  • PhD Mathematics, Imperial College London, 2014
  • MMath Mathematics, University of Warwick, 2010

Biography

Adam Thomas completed his MMath degree at the University of Warwick in 2010. He then studied for a PhD at Imperial College London, which he was awarded in 2014. He then held a one year research position at Imperial before moving to the University of Cambridge for six months. He was then a Heilbronn Research Fellow at the University of Bristol for three years before taking up his current position as a Research Fellow in Representation Theory at the University of Birmingham in 2018.

Research

Research Themes

  • Algebraic groups
  • Lie algebras
  • Finite groups of Lie type
  • Representation theory

Research Activity

Adam's research interests include group theory, Lie algebras and representation theory. A large amount of his work to date has centered around J.-P. Serre's notion of complete reducibility, a generalisation of the standard representation theoretic definition. This has played a key role in studying the structure of exceptional algebraic groups and their Lie algebras, especially in small characteristics. Adam has recently started to consider the representation theory of modular Lie algebras, in particular the study of W-algebras in positive characteristic.

Publications

  • Litterick, A. J., Thomas, A. R. (in press), Reducible subgroups of exceptional algebraic groups, J. Pure Appl. Algebra
  • Burness, T. C., Thomas, A. R. (2018), On the involution fixity of exceptional groups of Lie type, Int. J. Algebr. Comput., 28: 411-466.
  • Thomas, A. R. (in press), The irreducible subgroups of exceptional algebraic groups, Mem. Amer. Math. Soc.
  • Stewart, D. I., Thomas, A. R. (2018), The Jacobson-Morozov theorem and complete reducibility of Lie subalgebras, Proc. Lond. Math. Soc., 116: 68-100.
  • Litterick, A. J., Thomas, A. R. (2018), Complete reducibility in good characteristic, Trans. Amer. Math. Soc., 370: 5279-5340.
  • Liebeck, M. W., Thomas, A. R. (2017), Finite subgroups of simple algebraic groups with irreducible centralizers, J. Group Theory, 20: 841-870.   
  • Thomas, A. R. (2016), Irreducible A1 subgroups of exceptional algebraic groups, J. Algebra, 447: 240-296.
  • Thomas, A. R. (2015), Simple irreducible subgroups of exceptional algebraic groups, J. Algebra, 423: 190-238.