Research
Intersections of Dual SL3-Webs (with Linhui Shen and Daping Weng), preprint, arXiv:2311.15466, 31 pages.
Tropical Fock-Goncharov coordinates for SL3-webs on surfaces II: naturality (with Daniel Douglas), preprint, arXiv:2012.14202, 69 pages.
Volume of the moduli space of unmarked bounded positive convex RP2 structures, preprint, arXiv:2001.01295, 34 pages, very preliminary version.
Swapping algebra, Virasoro algebra and discrete integrable system, preprint, arXiv:1412.4330, 15 pages.
Publications
The Goldman symplectic form on the PGL(V)-Hitchin component (with Tengren Zhang), to appear in Mem. Amer. Math. Soc., arXiv 1709.03589.
Tropical Fock-Goncharov coordinates for SL3-webs on surfaces I: construction (with Daniel Douglas), Forum of Mathematics, Sigma (2024), Vol. 12:e5 1–55, arXiv 2011.01768.
McShane identities for Higher Teichmüller theory and the Goncharov-Shen potential (with Yi Huang), Mem. Amer. Math. Soc. 286 (2023), no. 1422. arXiv 1901.02032.
Rank n swapping algebra for Grassmannian, J. Algebr. Comb. 54 (2021), 1185–1199. arXiv 1904.06922.
Rank n swapping algebra for PGLn Fock--Goncharov X moduli space, Math. Ann. 380 (2021), 1311–1353. arXiv:1503.00918
Flows on the PGL(V)-Hitchin component (with Anna Wienhard and Tengren Zhang), Geom. Funct. Anal. 30 (2020), no. 2, 588–692. arXiv:1709.03580
Rank n swapping algebra for PSL(n,R) Hitchin component, Int Math Res Notices 2017.2 (2017), 583-613. arXiv:1411.2796
Rank n swapping algebra and its applications, PH. D. thesis under the direction of François Labourie at Universite de Paris-Sud, defended at 3 July 2014.
Survey etc
Survey on McShane identities for Higher Teichmüller theory and the Goncharov-Shen potential, survey contributed to the Proceedings of the 8th International Congress of Chinese Mathematicians.
Presentation slides
Introduction to Higher Teichmuller theory, slide.
Rank n swapping algebra and Fock-Goncharov coordinate, slide.
Deforming Hitchin component, Goldman symplectic form, slide.
McShane identities for Higher Teichmüller theory and the Goncharov-Shen potential, slide.
Volumes of subsets of PGL3(R)-Hitchin moduli space, slide.
Introduction to Higher Teichmuller theory (Fock-Goncharov’s approach), slide1, slide2.
Webs and tropical points on the surface, slide.