Research
Research Interests:
Research Interests:
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 Hitchin moduli space
Papers:
Papers:
[18](with Richard Wentworth, Boyu Zhang) Z2 harmonic 1-forms, R-trees and Morgan-Shalen compactification, arXiv:2409.04956
[18](with Richard Wentworth, Boyu Zhang) Z2 harmonic 1-forms, R-trees and Morgan-Shalen compactification, arXiv:2409.04956
, submitted.
, 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.
[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.
[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.
[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, to appear in Proceedings of the London Mathematical Society.
[14](with Jie Liu) The spectral variety of rank two Higgs bundle over projective variety, arXiv:2310.18198, to appear in Proceedings of the London Mathematical Society.
[13] (with Rafe Mazzeo, Xuesen Na, Richard Wentworth)The Algebraic and Analytic Compactifications of the Hitchin Moduli Space, arXiv:2304.08198, to appear in Moduli.
[13] (with Rafe Mazzeo, Xuesen Na, Richard Wentworth)The Algebraic and Analytic Compactifications of the Hitchin Moduli Space, arXiv:2304.08198, to appear in Moduli.
[11] The Branched Deformations of Special Lagrangian Submanifold, arXiv:2202.12282, GAFA, Volume 33, pages 1266–1321, (2023).
[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).
[10] On the Moduli Space of the Octonionic Nahm's Equations, arXiv:2006.11625, CAG, Volume 32, No 4, (2024).
[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.
[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.
[7] (with Rafe Mazzeo)Classification of Nahm pole solutions of the Kapustin-Witten equations on $S^1\times\Sigma\times R^+$, to appear in Transactions of the American Mathematical Society.
[7] (with Rafe Mazzeo)Classification of Nahm pole solutions of the Kapustin-Witten equations on $S^1\times\Sigma\times R^+$, to appear in Transactions of the American Mathematical Society.
[6] (with Thomas Walpuski)Hecke modifications of Higgs bundles and the extended Bogomolny equation, J. Geom. Phys. 146 (2019), 103487, 17 pp.
[6] (with Thomas Walpuski)Hecke modifications of Higgs bundles and the extended Bogomolny equation, J. Geom. Phys. 146 (2019), 103487, 17 pp.
[5] The Expansions of the Nahm Pole Solutions to the Kapustin-Witten Equations, arXiv:1808.03886, published as part of my Phd thesis.
[5] The Expansions of the Nahm Pole Solutions to the Kapustin-Witten Equations, arXiv:1808.03886, published as part of my Phd thesis.
[4] (with Rafe Mazzeo)The Extended Bogomolny Equations and Generalized Nahm Pole Solutions II, Duke Math Journal, 169 (2020), no. 12, 2281–2335.
[4] (with Rafe Mazzeo)The Extended Bogomolny Equations and Generalized Nahm Pole Solutions II, Duke Math Journal, 169 (2020), no. 12, 2281–2335.
[3] (with Rafe Mazzeo)The Extended Bogomolny Equations and Generalized Nahm Pole Solutions, Geometry &Topology, Volume 23, Number 5, 2019.
[3] (with Rafe Mazzeo)The Extended Bogomolny Equations and Generalized Nahm Pole Solutions, Geometry &Topology, Volume 23, Number 5, 2019.
[2] A Gluing Theorem for the Kapustin-Witten Equations with a Nahm Pole, Journal of Topology, Volume.12, Issue.3, 2019.
[2] A Gluing Theorem for the Kapustin-Witten Equations with a Nahm Pole, Journal of Topology, Volume.12, Issue.3, 2019.
[1] Rotationally Invariant Singular Solutions to the Kapustin-Witten Equations, Math Research Letters, Vol.25, no.4.
[1] Rotationally Invariant Singular Solutions to the Kapustin-Witten Equations, Math Research Letters, Vol.25, no.4.
Interdisciplinary collaborations:
Interdisciplinary collaborations:
[1] (with Yue Wang)Inference on autoregulation in gene expression, J. Math. Biol. 86 (2023), no. 5, Paper No. 87.
[1] (with Yue Wang)Inference on autoregulation in gene expression, J. Math. Biol. 86 (2023), no. 5, Paper No. 87.