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. 69 pages. To appear in Invent. Math.

**Preprints**

[8] Equivariant Eta Forms and Equivariant Differential K-Theory. 49 pages. arXiv:1610.02311.

[9] (with Xiaonan Ma) Comparison of two equivariant eta forms. 61 pages. arXiv:1808.04044.

**Notes **

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

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

*©
Dept. of Math. East China Normal University
*