Photographed in Iowa (2022)
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Email: zhub''at''tsinghua.edu.cn
2025--Present Assistant Professor, YMSC, Tsinghua University.
2022--2025 Visiting Assistant Professor, Texas A&M University. Mentor: Guoliang Yu (郁国梁).
2017--2022 Ph.D. University of Minnesota-Twin Cities. Advisor: Jiaping Wang (王嘉平).
Research Interest
Differential geometry, Coarse geometry and K-theory
Suggested reading books for undergraduate/graduate students in geometric analysis.
Differential geometry (basic textbooks)
Manfredo P. do Carmo, Differential Geometry of Curves and Surfaces, updated edition, Dover.
Manfredo P. do Carmo, Differential Forms and Applications, Springer.
Wolfgang Kühnel, Differential Geometry: Curves, Surfaces, Manifolds, 2nd edition, AMS.
陈维桓. 微分几何引论(2013). 高等教育出版社.
Alfred Gray, Tubes, 2nd edition, Birkhäuser.
Peter Petersen, Riemannian Geometry, 4th edition, Springer.
Allen Hatcher, Algebraic Topology (online available), Cambridge University Press.
Allen Hatcher, Vector Bundles and K-Theory (online available).
Partial differential equations (for geometric analysis)
David Gilbarg and Neil S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer.
Qing Han and Fanghua Lin, Elliptic Partial Differential Equations, 2nd edition, AMS.
Lawrence C. Evans, Partial Differential Equations, 2nd edition, AMS.
Advanced or professional geometry
Richard Schoen and Shing-Tung Yau, Lectures on Differential Geometry(微分几何讲义).
Peter Li, Geometric Analysis, Cambridge University Press.
Shing-Tung Yau, Perspectives in Geometric Analysis(online available).
Shing‑Tung Yau. Selected Expository Works of Shing‑Tung Yau with Commentary, Volumes I and II (Edited by Lizhen Ji, Peter Li, Kefeng Liu, Richard Schoen). ALM, Volume 28&29
M. Berger, A Panoramic View of Riemannian Geometry, Springer.
M. Berger, Riemannian Geometry During the Second Half of the Twentieth Century, AMS.
B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, Modern Geometry — Methods and Applications, Part I: The Geometry of Surfaces, Transformation Groups, and Fields, Springer.
B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, Modern Geometry — Methods and Applications, Part II: The Geometry and Topology of Manifolds, Springer.
B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, Modern Geometry — Methods and Applications, Part III: Introduction to Homology Theory, Springer.
M. Gromov, Metric Structures for Riemannian and Non-Riemannian Spaces, Birkhäuser.
Spin geometry and index theory
H. Blaine Lawson Jr. and Marie-Louise Michelsohn, Spin Geometry, Princeton University Press.
N. S. Teleman. From Differential Geometry to Non‑commutative Geometry and Topology(2019). Springer.
Guoliang Yu and Rufus Willett, Higher Index Theory, Cambridge University Press.
Alain Connes, Noncommutative Geometry (1994), Academic Press.
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