About me

Associate Professor at Shanghai Jiao Tong University.

My research interests include:
  • Cluster algebras 
  • Categorifications  (for example, via (graded/cyclic) quiver varieties, quiver Hecke algebras, etc.)
  • relations to quantum groups (canonical bases, representation theory), combinatoricstriangulated categories (Calabi-Yau categoeries), Donaldson-Thomas invariants and wall-crossing


School of mathematical sciences,
Shanghai Jiao Tong University,
800 Dongchuan road,
Shanghai, 200240


Publications / preprints

  • Bases for upper cluster algebras and tropical points, preprint, 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.
  • (joint 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.

Talk slides, notes, etc.


Useful tools

Free software
  • I use git for the version control of text files.
  • I have just started to use Lyx as the tex editor. Its spellchecker works, and the distinction between the equation mode and the text mode avoids the { } or $ $ unmatched bugs.
  • TikzEdt is convenient for drawing diagrams in latex.
  • For calculation on cluster algebras, I heavily depend on Bernhard Keller's application: quiver mutation in Java.
Proprietary software
  • I use Onenote (windows OS) for taking notes. I haven't found an open source and cross-platform alternative.
  • I use Dropbox and Evernote for collaboration.