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Liu, Bo's Resume

Resume and papers

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 and localization formula of eta invariants. Accepted in C. R. Acad. Sci. Paris.

Preprints
[7] Equivariant Eta Forms and Equivariant Differential K-Theory. 40 pages. arXiv:1610.02311.
[8] (with Xiaonan Ma) Differential K-theory and localization formula of eta invariants. 44 pages. arXiv:1808.03428.
[9] (with Xiaonan Ma) Comparison of two equivariant eta forms. 56 pages. arXiv:1808.04044.

Notes


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

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

 


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