Research

Preprints arXiv

Exponential volumes of moduli spaces of hyperbolic surfaces (with Alexander B. Goncharov), preprint, arXiv:2411.01615, 60 pages.      A talk given by Alexander B. Goncharov at IHES: link

Log-concavity of cluster algebras of type An (with Zhichao Chen and Guanhua Huang), preprint, arXiv:2408.03792, 26 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), Mem. Amer. Math. Soc. 312 (2025), no. 1585. arXiv 1709.03589.

Intersections of Dual SL3-Webs (with Linhui Shen and Daping Weng), Trans. Am. Math. Soc. 378 (2025), No. 8, 5513–5549. arXiv:2311.15466.

Tropical Fock-Goncharov coordinates for SL3-webs on surfaces II: naturality (with Daniel Douglas), Algebr. Comb. 8 (2025), no. 1, 101-156. arXiv:2012.14202.

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

Asymmetric intersection number and Fock–Goncharov duality, Teichmüller Theory: Classical, Higher, Super and Quantum. Oberwolfach Rep. 20 (2023), no. 3, pp. 1883-1886.

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.