My Research

Research Interests:

Currently I mainly work on non-Abelian Hodge theory related topics, more explicitly:

• Moduli spaces of Higgs bundles and local systems

• Applications to higher Teichmüller theory

But before, I had the interests on differential geometry, especially:

• Kobayashi-Hitchin correspondence for special bundles over special manifolds

• Gauge theory on manifolds with special holonomy

• Quiver representations and their moduli

Preprints and Publications:

♠︎. Moduli spaces of filtered (Stokes) G-local systems on curves (avec H. Sun), arXiv: 2304.09999  (New!)

♠︎. Meromorphic parahoric Higgs torsors and filtered Stokes G-local systems (avec H. Sun), arXiv: 2212.04939  (New!) accepted by Advances in Mathematics

♠︎. Tame parahoric nonabelian Hodge correspondence on curves (avec G. Kydonakis, H. Sun et L. Zhao), arXiv: 2205.15475  (New!)

♠︎. Moduli spaces of parabolic bundles over ℙ¹ with five marked points (avec Z. Hu et R. Zong), arXiv: 2108.08994

♣︎. Curvature formulas related to a family of stable Higgs bundles (avec Z. Hu), Communications in Mathematical Physics, 387 (2021), 1491-1514.

♣︎. Simpson filtration and oper stratum conjecture (avec Z. Hu), manuscripta mathematica, 167 (2022), 653-673. 

♠︎. Generalized Deligne-Hitchin twistor spaces: construction and properties (avec Z. Hu et R. Zong), arXiv: 2010.06893

♣︎. Non-Abelian Hodge theory and related topics, SIGMA, 16 (2020), 029, 34 pages. arXiv: 1908.08348 

♣︎. Simpson-Mochizuki correspondence for  λ-flat bundles (avec Z. Hu), Journal de Mathématiques Pures et Appliquées, 164 (2022), 57-92.

♣︎. The Hitchin-Kobayashi correspondence for quiver bundles over generalized Kähler manifolds (avec Z. Hu), Journal of Geometric Analysis, 30 (2020), 3641-3671.

♣︎. A note on fibrations of G₂-manifolds (avec Z. Hu), manuscripta mathematica, 160 (2019), 523-542. 

♣︎. Quivers from Higgs bundles over ℙ¹ and quiver gauge theory (avec Z. Hu), Journal of Mathematical Physics, 61 (2020), 011704. 

♣︎. Stability and indecomposability of the representations of A𝗇-type, Communications in Algebra, 48 (2020), 2905-2919. 

♣︎. Degenerate, strong and stable Yang-Mills-Higgs pairs (avec Z. Hu), Journal of Geometry and Physics, 120 (2017), 73-88.  

♣︎. A note on the space of Kähler metrics (avec Z. Hu), Journal of Geometry and Physics, 116 (2017), 1-9.  

Services:

Reviewer for Zentralblatt MATH (zbMATH) and Mathematical Reviews (MathSciNet).

Thesis:

Théorie de Hodge Non-Abélienne et des Spécialisations, defended on 12 June, 2020. Link here.