Siqi He

Research

Research interests

Low-dimensional topology and differential geometry: gauge theory with noncompact gauge group; Z/2 harmonic spinors and related geometry problems; Higgs bundles and the geometry of the Hitchin moduli space.

Papers

  1. (with Jiahuang Chen) Examples of Z/2-Harmonic 1-Forms, arXiv:2609.18915.
  2. (with Jie Liu, Siqing Zhang) Local obstructions to the surjectivity of spectral morphisms, arXiv:2609.17139.
  3. (with Jiahuang Chen, Willem Adriaan Salm) Prescribed Singular Sets for Z/2-Harmonic 1-Forms on Rn, arXiv:2609.13059.
  4. (with Greg Parker, Thomas Walpuski) The universal moduli space of non-degenerate Z/2 harmonic spinors, arXiv:2609.02848.
  5. (with Jiahuang Chen, Dashen Yan) Calabi Surgery for Z/2 harmonic 1-forms, arxiv:2607.24281, submitted.
  6. (with Willem Adriaan Salm, Andriy Haydys) Deformation rigidity for Z/2 eigensections, arxiv:2604.17044, submitted.
  7. (with Willem Adriaan Salm) Metric perturbations and deformations of k-nondegenerate Z/2-harmonic 1-forms, arxiv:2603.14949, submitted.
  8. (with Jiahuang Chen) On the non-Archimedean Hitchin map for SL2(F), arXiv:2511.03469, submitted.
  9. (with Johannes Horn, Nianzi Li) The asymptotics of the SL2(C)-Hitchin metric on the singular locus: subintegrable systems, arXiv:2506.04957.
  10. (with Richard Wentworth, Boyu Zhang) Z2 harmonic 1-forms, R-trees and Morgan-Shalen compactification, arXiv:2409.04956, to appear Inventiones Mathematicae
  11. (with Greg Parker) Connect sum and torus sum formulas for Z2 harmonic spinors and 1-forms on 3-manifolds, arXiv:2407.10922, to appear, Geometry&Topology.
  12. (with Jiahuang Chen) On the existence and rigidity of critical Z2 eigenvalues, arXiv:2404.05387, submitted.
  13. (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:2310.18934, Proc. Lond. Math. Soc. (3) 129 (2024), no. 5, Paper No. e70004, 45 pp.
  15. (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.
  16. Existence of nondegenerate Z2 harmonic 1-forms via Z3 symmetry, arXiv:2202.12283, Geom. Dedicata 219 (2025), no. 2, Paper No. 28, 13 pp.
  17. The Branched Deformations of Special Lagrangian Submanifold, arXiv:2202.12282, GAFA, Volume 33, pages 1266–1321, (2023).
  18. On the Moduli Space of the Octonionic Nahm's Equations, arXiv:2006.11625, CAG, Volume 32, No 4, (2024).
  19. The behavior of sequences of solutions to the Hitchin-Simpson equations, arXiv:2002.08109, submitted.
  20. (with Rafe Mazzeo) Opers and the twisted Bogomolny equations, arXiv:1902.11183, Ann. Sci. Éc. Norm. Supér. (4) 55 (2022), no. 5, 1329–1356.
  21. (with Rafe Mazzeo) Classification of Nahm pole solutions of the Kapustin-Witten equations on S1 × Σ × R+, to appear in Transactions of the American Mathematical Society.
  22. (with Thomas Walpuski) Hecke modifications of Higgs bundles and the extended Bogomolny equation, J. Geom. Phys. 146 (2019), 103487, 17 pp.
  23. The Expansions of the Nahm Pole Solutions to the Kapustin-Witten Equations, arXiv:1808.03886, published as part of my Phd thesis.
  24. (with Rafe Mazzeo) The Extended Bogomolny Equations and Generalized Nahm Pole Solutions II, Duke Math Journal, 169 (2020), no. 12, 2281–2335.
  25. (with Rafe Mazzeo) The Extended Bogomolny Equations and Generalized Nahm Pole Solutions, Geometry &Topology, Volume 23, Number 5, 2019.
  26. A Gluing Theorem for the Kapustin-Witten Equations with a Nahm Pole, Journal of Topology, Volume.12, Issue.3, 2019.
  27. Rotationally Invariant Singular Solutions to the Kapustin-Witten Equations, Math Research Letters, Vol.25, no.4.

Interdisciplinary collaborations

  1. (with Yue Wang) Inference on autoregulation in gene expression, J. Math. Biol. 86 (2023), no. 5, Paper No. 87.