Senior lecturer in Mathematics
University of Bath
Bath BA2 7AY, U.K.
Phone: +44 (0)1225 384738
E-mail: xs214 at bath.ac.uk
My research interests are quiver
representation theory (or representation theory of associative algebra) and its
related topics. Quiver representation theory has broad connections to various
research areas in mathematics, e.g. Kac-Moody Lie
algebras, quantum groups, cluster algebras and algebraic geometry. In particular, I have been working on the following topics:
tame behaviour of wild quivers, degeneration orders in derived categories,
Grassmannian cluster algebras and the connections between quivers, Lie theory
and q-Schur algebras. ...to be continued.
EPSRC 1st Grant: EP/1022317/1, Generic
points in representation varieties with applications to Lie theory and 0-Schur
· Tom Crawley (09.2016-12.2020), Double affine flag varieties and
affine 0-Schur algebras
· Robert Brown (09.2017-08.2021), Delta-filtered representations of
a class of double quivers and seaweed Lie algebras of affine type A
· Liam Riodan (09.2021-)
that I have taught:
- MA 10210 Algebra 1B
- MA 6000P Quantum groups and Hall algebras
- MA 40233 Topics in Pure Maths
- MA 40037 Galois Theory
- MA 40054 Representation theory of finite groups
- MA 30204/50204 Algebraic Structures
- MA 10104 Foundation Mathematics 2
- MA 6000P Lie algebras
Preprints and Publications
- The Auslander-Reiten quivers
of string algebras of affine type C and a conjecture by Geiss-Leclerc-Schroeer (with H. Huang and Z. Lin). arXiv 2110.02777. Submitted.
- Categorification and the quantum Grassmannians (with B.
T. Jensen and A. King). arXiv 1904.07849.
Advances in Mathematics 406 (2022).
- Richardson elements for seaweed Lie algebras of type B,
C, D. (with B. T. Jensen). arXiv 1601.01755.
Journal of LMS, 2019
- Presenting Hecke endomorphism algebras by Hasse quivers with relations (with B. T. Jensen and J.
Du). arXiv 1511.04135.
Journal of Pure and Applied Algebra, 2017.
- Degenerate 0-Schur algebras and nil-Hecke algebras
(with B. T. Jensen and G. Yang). Algebras and Representation Theory, 2019.
- Projective modules of 0-Schur algebras. (with B. T. Jensen and G. Yang). Preprint arXiv: 1312.5487. Journal of Algebra, 2016.
- A category for grassmannian
cluster algebras (with B. T. Jensen and A. King). Preprint arXiv 1309.7301. Proceedings of the LMS, 2016.
- A geometric Construction of 0-Schur algebras and
0-Hecke algebras (with B. T. Jensen). Journal of Pure and Applied Algebra,
219 (2), pp. 277-307.
- Adjoint action of automorphism groups on radical
endomorphisms, generic equivalence and Dynkin
quivers (with B. T. Jensen).
arXiv:1002.4432. Algebras and Representation Theory, 17 (4), pp. 1095-1136.
- Filtrations in abelian categories with a tilting object
of homological dimension two (with B. T. Jensen and D. Madsen).
Journal of Algebra and its Applications, Vol. 12, No. 02 (2013). PDF
- A generic multiplication in quantized Schur algebras, Q
J Math (2010) 61 (4): 497-510. PDF
- Exceptional representations of a double of quivers of
type A, and Richardson elements in Seaweed Lie algebras (with B. T. Jensen
and R. Yu), Bull. Lond. Math. Soc.41(2009), no.
1, 1-15. PDF. A complete version PDF.
- Degeneration of A-infinity modules (with B. T. Jensen
and D. Madsen), Trans. Amer. Math. Soc. 361(2009), no.8, 4125-4142. PDF
- Indecomposable representations for real roots of a wild
quiver (with B. T. Jensen), Journal of Algebra 319(2008), 2271-2294.
- Flatness for the moment map for representations of
quivers, Journal of Algebra 298(2006) 105-119.
- Singularities in derived categories (with B. T.
Jensen), Manuscripta Mathematica, 117 (2005),
no. 4, 475--490. PDF
- Degeneration-like order in triangulated categories
(with B. T. Jensen and A. Zimmermann), Journal of Algebra and its
Vol. 4, No. 5(2005)587-597.
- Degenerations for derived categories (with B. T. Jensen
and A. Zimmermann), Journal of Pure and Applied Algebra, Vol. 198(2005),
Issues 1-3, 281-295.
- Tame roots of wild quivers, Journal of Algebra 280
(2004), no. 2, 590--609.
- Tame roots of wild quivers and their representations(PhD
thesis, 06. 2002).
- The existence of tame roots and their properties(Chinese), Beijing Shifan
Daxue Xuebao 38
(2002), no. 6, 714-719.
- The number of exceptional sequences of types D and
E(Chinese), Xiamen Daxue Xuebao
Ziran Kexue Ban 37
(1998), no. 6, 802--806.
- The number of complete exceptional sequences of type A(with Y. Lin)(Chinese), Xiamen Daxue
Xuebao Ziran Kexue Ban 37 (1998),
no. 4, 469--472.