About Research Teaching Events 中文版

Topics:

  1. I mainly work on mathematical physics involving:
    Index theory on manifolds, Intersection theory on moduli spaces.

  2. I am also interested in:
    Arithmetic geometry, Complex geometry, Geometric analysis, High energy physics, LLM, PDE, Random matrices, Statistics, Symplectic geometry.

Accepted Papers:

  1. Mapping cone Thom forms.
    Peking Mathematical Journal (2026).
    DOI: 10.1007/s42543-026-00133-6.
    arXiv: 2603.25087.

  2. Symplectic semi-characteristics.
    Pacific Journal of Mathematics 343-2 (2026), 485-507.
    DOI: 10.2140/pjm.2026.343.485.
    MathSciNet: MR5076564.
    arXiv: 2505.14496.

Preprints on arXiv:

  1. Odd mapping cone Chern character.
    arXiv: 2610.20300v1. Submitted.

  2. Bott connection in the mapping cone case.
    arXiv: 2609.07007v1. Submitted.

  3. Instanton construction of the mapping cone Thom-Smale complex.
    arXiv: 2603.08404v3. Submitted.

  4. A Serre type vanishing property of the twisted primitive cohomology.
    arXiv: 2605.21410v1. Submitted.

  5. Transgression in the primitive cohomology.
    arXiv: 2512.24920v1. Submitted.

  6. A vanishing property about the 1-filtered cohomology groups of (4n+2)-dimensional closed symplectic manifolds.
    arXiv: 2510.10630v1. Submitted.

  7. Analytic and topological realizations of the invariant Thom-Smale complex.
    arXiv: 2311.10417v5. Part 1 of my thesis. Submitted.

  8. Kervaire semi-characteristics in KK-theory and an Atiyah type vanishing theorem.
    arXiv: 2410.00794v2. Part 2 of my thesis. Submitted.

Math Fictions:

  1. Happy π Day: 自然的期望, 我们的希望 (in Chinese).