Dr Matthew Westaway MMath PhD

Dr Matthew Westaway

School of Mathematics
Research Fellow in Representation Theory
Royal Commission for the Exhibition of 1851 Fellow

Contact details

Address
School of Mathematics
Watson Building
University of Birmingham
Edgbaston
Birmingham
B15 2TT
UK

Matthew Westaway is a research fellow in the School of Mathematics, working with Dr Simon Goodwin on the subject of representation theory of Lie algebras in positive characteristic. He started this position in 2020, after completing his PhD at the University of Warwick that same year. He has published seven research papers, with one more currently being reviewed by a journal and others in preparation. In October 2021, he started a research fellowship at the University of Birmingham funded by the Royal Commission for the Exhibition of 1851.

Qualifications

  • PhD in Mathematics, University of Warwick, 2020
  • MMath in Mathematics, University of Warwick, 2016

Biography

Matthew Westaway completed an MMath at the University of Warwick from 2012 to 2016. In his final year, he completed a research project which was subsequently published in the Journal of Algebra. He graduated with a First in 2016, but he remained at the University of Warwick for postgraduate study.

From 2016 to 2020, he completed a PhD in Warwick under the supervision of Drs Dmitriy Rumynin and Inna Capdeboscq. During his PhD, he completed 6 research papers, individually and with collaborators, 4 of which have been published and 2 of which are currently being reviewed at journals. He graduated in 2020, after submitted his thesis entitled 'Modular Representation Theory of Algebraic Groups and Their Lie Algebras'.

He started a research fellowship at the University of Birmingham in 2020, working with Dr Simon Goodwin on the subject of representations of Lie algebras and W-algebras in positive characteristic.

In 2021, he was awarded a research fellowship by the Royal Commission for the Exhibition of 1851 for a project entitled 'Simple representations of modular Lie algebras,' which he has held at the University of Birmingham from October 2021.

Research

Research Themes

  • Reduced enveloping algebras of Lie algebras
  • Representations of algebraic groups in positive characteristic
  • Hopf algebras
  • Categorical actions
  • Induction theorems

Research Activity

Matthew’s research focuses on the study of representations of Lie algebras in positive characteristic. He is interested in the connection between this theory and the theory of D-modules, as well as the ways in which category theory can be utilized to prove results in this area. Relatedly, he studies the interplay between modules over algebraic groups and modules over their Lie algebras.

Publications

Recent publications

Article

Westaway, M 2022, 'On graded representations of modular Lie algebras over commutative algebras', Journal of Pure and Applied Algebra. <https://arxiv.org/abs/2106.04994>

Rumynin, D & Westaway, M 2021, 'Centrification of algebras and Hopf algebras', Canadian Journal of Mathematics. https://doi.org/10.4153/S0008439521000175

Westaway, M 2021, 'Higher deformations of lie algebra representations II', Nagoya Mathematical Journal, vol. 244, pp. 232-255. https://doi.org/10.1017/nmj.2020.13

Rumynin, D & Westaway, M 2021, 'Integration of modules – II: exponentials', Transactions of the American Mathematical Society, vol. 374, no. 10, pp. 6797-6813. https://doi.org/10.1090/tran/8449

Westaway, M, Rumynin, D & Vakhrameev, D 2019, 'Covering groups of nonconnected topological groups and 2-groups', Communications in Algebra, vol. 47. https://doi.org/10.1080/00927872.2019.1612425

Westaway, M & Rumynin, D 2019, 'Integration of modules I: stability', Pacific Journal of Mathematics, vol. 301. https://doi.org/10.2140/pjm.2019.301.575

Westaway, M 2018, 'Higher Deformations of Lie Algebra Representations I', Journal of the Mathematical Society of Japan, vol. 73. https://doi.org/10.2969/jmsj/81188118

Westaway, M 2017, 'K 2 of Kac–Moody groups', Journal of Algebra, vol. 484. https://doi.org/10.1016/j.jalgebra.2017.03.024

View all publications in research portal