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 algebras.
Courses 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
- Richardson elements for seaweed Lie algebras of type B,
C, D. (with B. T. Jensen). arXiv
- Presenting Hecke endomorphism
algebras by Hasse quivers with relations (with
B. T. Jensen and J. Du). arXiv
To appear in Journal of Pure and Applied Algebra.
- Degenerate 0-Schur algebras and nil-Hecke
algebras (with B. T. Jensen and G. Yang). Submitted.
- Projective modules of 0-Schur algebras. (with B. T. Jensen and G. Yang). Preprint arXiv: 1312.5487. To appear in Journal of Algebra.
- A category for grassmannian
cluster algebras (with B. T. Jensen and A. King). Preprint arXiv 1309.7301. To appear in Proceedings of the LMS.
- 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.
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).
To appear in Journal of Algebra and its Applications. 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.