Bo Liu's Homepage

Research Fields

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.

Education

2007, Bachelor's degree, Mathematics, University of Science and Technology of China.

2010, Master's degree, Mathematics, Chern Institute of Mathematics, Nankai University of China.

2013, Ph.D., Mathematics, Chern Institute of Mathematics, Nankai University of China.

Work Experience

2014-2016 Postdoc: Universität zu Köln; Humboldt-Universität zu Berlin in Germany.

2017-2019 Postdoc in East China Normal University.

2019-2020 Young Researcher in ECNU.

2021- Professor in ECNU.

Publications

[1] (with Jianqing Yu) On the Anomaly Formula for the Cappell-Miller Holomorphic Torsion. Sci. China Math.. 2010, 53(12): 3225-3241. [pdf]

[2] (with Jianqing Yu) On the Witten Rigidity Theorem for Stringc Manifolds. Pacific J. Math., 2013, 266(2): 477-508. [pdf]

[3] (with Jianqing Yu) Rigidity and Vanishing Theorems on Z/k Spinc manifolds. Trans. Amer. Math. Soc. 2015, 367(2), 1381–1420. [pdf]

[4] Functoriality of Equivariant Eta Forms. Journal of Noncommutative Geometry. 2017, 11(1), 225-307. [pdf]

[5] Real embedding and Equivariant Eta Forms. Math. Z. 292 (2019), 849-878. [pdf]

[6] (with Xiaonan Ma) Differential K-theory, eta-invariant, and localization. C. R. Math. Acad. Sci. Paris. 357(10) (2019), 803--813. [pdf]

[7] (with Xiaonan Ma) Differential K-theory and localization formula of eta invariants. Invent. Math. 222(2) (2020), 545-613. [pdf]

[8] Equivariant Eta Forms and Equivariant Differential K-Theory. Sci. China Math. 64(10) (2021), 2159-2206. [pdf]

[9] (with Xiaonan Ma) Comparison of two equivariant eta forms. Adv. Math. 404 (2022), paper No. 108163. 76pp. [pdf]

[10] Bismut-Cheeger eta form and higher spectral flow. IMRN. 2023(13), (2023), 10964-10996. [pdf]