![bliu](/~bliu/images/people.jpg)
职称: | 教授,博导,国家级高层次人才计划入选者 |
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所属部门: | 基础数学系 |
办公室: | 闵行数学楼322室 |
办公电话: | 54342646-322 |
邮箱: | bliu@math.ecnu.edu.cn |
个人主页: | http:/~bliu |
学校名录: | https://faculty.ecnu.edu.cn/_s42/lb2/main.psp |
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)
Teaching:
Undergraduates:
Autumn 2019: Mathematical Analysis I
Spring 2020: Mathematical Analysis II
Autumn 2020: Mathematical Analysis III
Spring 2021: Differential Geometry
Spring 2022: Differential Geometry
Graduates:
Spring 2018: Complex Manifolds and Kaehler Geometry
Spring 2019: Analysis on manifolds
Spring 2020: Riemannian Geometry
Autumn 2020: Introduction to Lie groups