Low dimensional topology and differential geometry: Gauge theory with noncompact gauge group; Z/2 harmonic spinor and related geometry problems; Higgs bundles and the geometry of the Hitchin moduli space.
Papers:
[19](with Johannes Horn, Nianzi Li)The asymptotics of the SL2(C)-Hitchin metric on the singular locus: subintegrable systems, arXiv:2506.04957.
[18](with Richard Wentworth, Boyu Zhang) Z2 harmonic 1-forms, R-trees and Morgan-Shalen compactification, arXiv:2409.04956
, submitted.
[17](with Greg Parker) Connect sum and torus sum formulas for Z2 harmonic spinors and 1-forms on 3-manifolds, arXiv:2407.10922, submitted.
[16](with Jiahuang Chen) On the existence and rigidity of critical Z2 eigenvalues, arXiv:2404.05387, submitted.
[15](with Jie Liu, Ngaiming Mok) The spectral base and quotients of bounded symmetric domains by cocompact lattices, arXiv:2401.15852, submitted.
[14](with Jie Liu) The spectral variety of rank two Higgs bundle over projective variety, arXiv:2310.18198, Proc. Lond. Math. Soc. (3) 129 (2024), no. 5, Paper No. e70004, 45 pp.
[13] (with Rafe Mazzeo, Xuesen Na, Richard Wentworth)The Algebraic and Analytic Compactifications of the Hitchin Moduli Space, arXiv:2304.08198, Moduli 1 (2024), Paper No. e2, 45 pp.
[12] Existence of nondegenerate Z2 harmonic 1-forms via Z3 symmetry, arXiv:2202.12283, Geom. Dedicata 219 (2025), no. 2, Paper No. 28, 13 pp.
[11] The Branched Deformations of Special Lagrangian Submanifold, arXiv:2202.12282, GAFA, Volume 33, pages 1266–1321, (2023).
[10] On the Moduli Space of the Octonionic Nahm's Equations, arXiv:2006.11625, CAG, Volume 32, No 4, (2024).
[9] The behavior of sequences of solutions to the Hitchin-Simpson equations, arXiv:2002.08109, submitted.
[8] (with Rafe Mazzeo)Opers and the twisted Bogomolny equations, arXiv:1902.11183, Ann. Sci. Éc. Norm. Supér. (4) 55 (2022), no. 5, 1329–1356.