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About me

I am a mathematician working on algebras and representation theory.

I am interested in cluster algebras and their relation to other research topics, including quantum groups, algebraic and geometric representation theory, categorification, algebraic geometry, tropical geometry and (higher) Teichmüller theory.

Publications / preprints

  • An analog of Leclerc's conjecture for bases of quantum cluster algebras, SIGMA 16 (2020), 122, DOI:10.3842/SIGMA.2020.122.

  • Dual canonical bases and quantum cluster algebras, preprint, arXiv:2003.13674.

  • Bases for upper cluster algebras and tropical points, Journal of the European Mathematical Society, to appear, arXiv:1902.09507.

  • Compare triangular bases in acyclic quantum cluster algebras, Transactions of the American Mathematical Society, Volume 372, Number 1 (2019), 485-501, DOI:10.1090/tran/7610 .

  • Triangular bases in quantum cluster algebras and monoidal categorification conjectures, 106 pages, Duke Mathematical Journal, Volume 166, Number 12 (2017), 2337-2442, DOI:10.1215/00127094-2017-0006.

  • Quantum groups via cyclic quiver varieties I, Compositio mathematica 152 (2016), no. 2, 299--326, DOI:10.1112/S0010437X15007551.

  • t-analog of q-characters, bases of quantum cluster algebras, and a correction technique, International Mathematics Research Notices 2014 (2014), no. 22, 6175--6232, DOI:10.1093/imrn/rnt115.

  • (with Yoshiyuki Kimura) Graded quiver varieties, quantum cluster algebras, and dual canonical basis, Advances in Mathematics 262 (2014), 261--312, DOI:10.1016/j.aim.2014.05.014.

  • (appendix by Bernhard Keller) Quantum cluster variables via Serre polynomials, Journal für die reine und angewandte Mathematik (Crelle's Journal) 668 (2012), 149--190, DOI:10.1515/CRELLE.2011.129.

Proceedings

  • Cluster algebras and their bases, proceedings of ICRA2020, to appear, arXiv:2108.09279.


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Contact

  • Email: qin.fan.math AT gmail.com

  • Postal address: The School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dongchuan RD, Shanghai, 200240 China.