About Me
I am a Neumann Fellow at the University of Manchester. Before this I held the following posts:
- Assistant Professor (RTPC) at the University of Southern California,
- Postdoctoral Research Associate at the University of Arizona,
- Marie Curie fellow of the Istituto Nazionale di Alta Matematica based at the Università degli Studi di Padova,
- Postdoctoral researcher at the EPFL as part of the working group of Donna Testerman,
- Wissenschaftlicher Mitarbeiter at the TU Kaiserslautern as part of the working group of Gunter Malle.
For more information please see my CV.
Want To Know What I Do?
Together with my colleague Eugenio Giannelli we wrote the following "Snapshot of Modern Mathematics from Oberwolfach". It is an accesible, short, introduction to the representation theory of finite groups aimed at the level of an advanced high school student.
- Symmetry and Characters of Finite Groups, Snapshots of Modern Mathematics from Oberwolfach (2016), no. 5.
Recent Output
Preprint versions of all articles, together with links to the published versions, are available on the papers page.
- Harish-Chandra Cuspidal Pairs, Indag. Math. (N.S.), in press.
- Galois Automorphisms and Classical Groups, 43 pages, preprint available here and at arXiv:2005.14088. (with A. A. Schaeffer Fry).
- Unitriangular Shape of Decomposition Matrices of Unipotent Blocks, Ann. of Math. (2) 192 (2020), no. 2, 583–663. (with O. Brunat, and O. Dudas).
- Lusztig Induction, Unipotent Supports, and Character Bounds, Trans. Amer. Math. Soc. 373 (2020), no. 12, 8637–8676. (with P. H. Tiep).
- Principal 2-Blocks and Sylow 2-Subgroups, Bull. Lond. Math. Soc. 50 (2018), 733–744. (with A. A. Schaeffer Fry).
- The Structure of Root Data and Smooth Regular Embeddings of Reductive Groups, Proc. Edinb. Math. Soc. (2) 62 (2019), no. 2, 523–552.
Software
I have an avid interest in programming and computational problems concerning finite reductive groups. I am in the process of developing CharLiePy, which is a mix of Python code and handwritten C extensions for improved computational efficiency. More information about CharLiePy can be found by reading the documentation.
Research Interests
My main research interests are in Deligne-Lusztig theory. One overall aim of this theory is to understand the representations of finite reductive groups using geometric methods. In particular I am interested in:
- finite reductive groups with a disconnected centre,
- character sheaves,
- generic ordinary character tables of finite reductive groups,
- unipotent conjugacy classes and unipotent supports,
- generalised Gelfand–Graev representations (GGGRs).
Education
I completed my PhD at the University of Aberdeen, in the department of Mathematics. I started this endeavour in October 2008 and finished in April 2012 under the supervision of Meinolf Geck. The focus of my PhD was on unipotent supports for ordinary characters of finite reductive groups with a disconnected centre.
I did my first degree at the University of York, where I was supervised by Stephen Donkin for my MMath project. It was in this supervision period that I was first introduced to the theory of algebraic groups.