Seminar of differential geometry in ECNU

Research field

Differential Geometry.

Special interests

Global analysis on manifolds, local index theory and differential K-theory.

Main research objects

Analytic and differential-topological properties of Atiyah-Patodi-Singer eta-invariant, Bismut-Cheeger eta form, Ray-Singer analytic torsion, elliptic genera and related objects, especially on relations between eta forms and differential K-theory.

Employment history
Postdoc: Universität zu Köln; Humboldt-Universität zu Berlin in Germany.

Visit
2017.1 Institut des Hautes Études Scientifiques (IHES), France;
2017.3 Max Planck Institute for Mathematics (MPIM), Germany;
2017.5 University of California, Santa Barbara, USA
2018.5 Institut de Mathematiques de Jussieu, France.

Education

2013.12 Ph.D., Mathematics, Chern Institute of Mathematics, Nankai University of China. (Advisor: Prof. Weiping Zhang)

Publications
[1] (with Jianqing Yu) On the Anomaly Formula for the Cappell-Miller Holomorphic Torsion. Sci. China Math.. 2010, 53(12): 3225-3241.
[2] (with Jianqing Yu) On the Witten Rigidity Theorem for Stringc Manifolds. Pacific J. Math., 2013, 266(2): 477-508.
[3] (with Jianqing Yu) Rigidity and Vanishing Theorems on Z/k Spinc manifolds. Trans. Amer. Math. Soc. 2015, 367(2), 1381–1420.
[4] Functoriality of Equivariant Eta Forms. Journal of Noncommutative Geometry. 2017, 11(1), 225-307.
[5] Real embedding and Equivariant Eta Forms. Math. Z. 292 (2019), 849-878.
[6] (with Xiaonan Ma) Differential K-theory, eta-invariant, and localization. C. R. Math. Acad. Sci. Paris. 357(10) (2019), 803--813.
[7](with Xiaonan Ma) Differential K-theory and localization formula of eta invariants. Invent. Math. 222(2) (2020), 545-613.
[8] Equivariant eta forms and equivariant differential K-theory. Sci. China Math. 64(10) (2021), 2159-2206.
[9] (with Xiaonan Ma) Comparison of two equivariant eta forms. 61 pages. arXiv:1808.04044. To appear in Advances in Mathematics

Preprints
[10] Bismut-Cheeger eta forms and higher spectral flow. arXiv:2105.01926.

Notes

[1] Complex manifold and Kaehler geometry (2018 spring course)

[2] Global analysis on manifolds (2019 spring course)