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My interests are in diagrammatic algebra and 2-categorical Lie theory.  Examples of the objects I study are symmetric groups, KLR algebras, algebraic groups, Khovanov arc algebras, and Hecke categories.  My research is currently supported by EPSRC early career fellowship EP/V00090X/1.

I am a reader at the University of York.  Before this, I was a reader at the University of Kent, I held a research fellowship from Royal Commission for the Exhibition of 1851 at City University of London, and I had a postdoc with Eric Vasserot at Paris 7.  My PhD was at Corpus Christi College Cambridge, 2008-2012.  


Selected publications


Path isomorphisms between quiver Hecke and diagrammatic Bott--Samelson endomorphism algebras, joint with A. Cox and A. Hazi, Advances in Mathematics 2023 (106 pages).  

This paper solves Libedinsky-Plaza's conjecture from 2018 and calculates decomposition numbers of cyclotomic Hecke algebras in terms of p-Kazhdan-Lusztig polynomials. (There is a sign error in the definition of breadth in the published version, see arXiv.)


Unitary representations of cyclotomic Hecke algebras at roots of unity: combinatorial classification and BGG resolutions, joint with E. Norton and J. Simental, Journal of the Institute of Mathematics of Jussieu 2022 (52 pages).

This paper extends Berkesh-Griffeth-Sam's conjecture to all cyclotomic Hecke algebras by classifying and constructing all unitary modules of these algebras via BGG resolutions. 

On BGG resolutions of unitary simple modules for quiver Hecke and Cherednik algebras, joint with E. Norton and J. Simental, Selecta Mathematica 2022 (71 pages). 

This paper solves Berkesh-Griffeth-Sam's conjecture from 2013 by providing BGG resolutions of homogeneous representations of cyclotomic KLR algebras.

The many graded cellular bases of Hecke algebras, American Journal of Mathematics, 2022 (67 pages)

This paper solves Martin-Woodock's conjecture from 2000 and completes Geck-Rouquier's canonical basic set programme for Lusztig orderings on multipartitions.

Multiplicity-free Kronecker products of characters of the symmetric groups, joint with C. Bessenrodt, Advances in Mathematics, 2017 (56 pages).  

This paper solves Bessenrodt's conjecture from 1999 by classifying and constructing all multiplicity-free tensor products of characters of symmetric groups.