**Xiuping Su**

Senior lecturer in Mathematics

Mathematical
Sciences |
Office:
4W 5.14 |

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.

**Research grant**

EPSRC 1st Grant: EP/1022317/1, Generic points in representation varieties with applications to Lie theory and 0-Schur algebras.

**PhD students**

· 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-)

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

- 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
Applications,

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.