硕 导 个 人 简 介







◆ 个人简介
刘克峰，教授，硕士生导师，加州大学洛杉矶分校和浙江大学博士生导师。
1985.7，北京大学数学系学习，获理学学士学位
1988.7，中科院数学研究所学习，获理学硕士学位
1993,7，美国哈佛大学数学系学习，获哲学博士学位
1993.9-1996.7 美国麻省理工学院（MIT）Moore 讲师
1996.9-2000.7 美国斯坦福大学（Stanford University）助理教授
2000.9-2002.7 美国加州大学洛杉矶分校（UCLA）副教授
2002.9-至今 美国加州大学洛杉矶分校（UCLA）教授
美国大学短学期无薪休假兼职:
2003.7-至今 任浙江大学数学中心执行主任、首批光彪讲座教授；
2004.9-2009.7浙江大学数学系主任。
2019.7-至今 任重庆理工大学数学科学研究中心主任

刘克峰教授在微分几何、拓扑、数学物理等研究方向取得了大量国际一流的原始创新成就，其研究工作与阿蒂亚-辛格指标定理、费马大定理证明这两项二十世纪最伟大的数学成就有着深刻的联系。刘克峰教授先后在《PNAS》、《J. Amer. Math. Soc.》、《Invent. Math.》、《Duke Math. J.》、《J. Differential Geom.》等最有影响的国际一流杂志上发表学术论文130余篇。现任国际著名数学杂志《Comm. Analysis and Geometry》、《Pure and Appl. Math. Quartly》主编，《Pacific J. Math.》、《Asian J. Math.》编委。荣获了全球华人数学最高奖“晨兴数学金奖”和2004年中国高校十大科技进展。获得了国际上著名的谷庚海默奖、全球华人数学家大会银奖、Sloan奖、Terman奖等多项重要国际奖项，谷庚海默奖是颁发给取得重大成就的美国科学家、艺术家、作家的最高奖项之一，获奖者被授予谷庚海默院士称号，许多诺贝尔奖、菲尔兹奖获得者先后获得过这一大奖。先后多次应邀在重要国际学术会议上作大会报告和特邀报告，其中包括2002年国际数学家大会特邀报告、2001年国际华
人数学家大会大会报告等。自1994年起，一直主持承担美国国家科学基金项目等重要科研项目。被评选为中国科学院海外知名****、中国科学院核心数学挑战性问题国际研究团队学术带头人。他还是国家****基金(B类)获得者。
◆ 研究领域
Modular invariance, Kac-Moody algebras, Mathematical physics, Geometry and Topology
◆ 承担的主要项目
[1] Geometry of Deformation and Moduli Spaces of Complex Manifolds, National Science Foundation, 2015-2019
[2] Geometry and Topology of moduli spaces of Riemann Surfaces & Calabi-Yau manifold, NSF DMS-**, 2010-2013
[3] Localication, String Duality and Moduli Spaces, National Science Foundation , 2007-2009
[4] Strings, National Science Foundation, 2006
[5] Mathematical Aspects of String Duality, National Science Foundation, 2004-2007
[6] Distinguished Scholar Grant, Chinese Academy of Science, 2003-2004
[7] Research Grant, ZhejiangUniversity, 2002-2004
[8] Top. of Counting Curves in Proj. Man., National Science Foundation, 2000-2003。

◆ 代表性成果
[1] K. Liu, On Mod 2 and Higher Elliptic Genera. Comm. in Math. Physics, 149(1), 1992, 71-97
[2] K. Liu, On Elliptic Genera and Theta-Functions. Topology, 35(3), 1992, 617-640
[3] K. Liu, On Modular Invariance and Rigidity Theorems. J. of Diff. Geom., 41, 1995, 343-396,
[4] K. Liu, On SL2(Z) and Topology. Math. Research Letters, 1(1), 1994, 53-64
[5] K. Liu, Modular Forms and Topology. In Proc. of the AMS Conference on the Monster and Related Topics, Contemporary Math., 193, 1996, 237-262
[6] K. Liu, Holomorphic Equivariant Cohomology. Math. Ann., 303, 1995, 125-148
[7] B. Lian, K. Liu, S.-T. Yau, The Candelas-de la Ossa-Green-Parkes Formula. In String Theory, Gauge Theory, and Quantum Gravity, Trieste 1997, Nuclear Phys. B Proc. Suppl., 67, 1998, 106-114
[8] B. Lian, K. Liu, S.-T. Yau, Mirror Principle I, II, III. Asian J. Math., 1, 1997, 729-763; 3, 1999, 109-146; 4, 1999, 771-800
[9] K. Liu, X. Ma, On Family Rigidity Theorems I.. Duke Math. J., 102, 2000, 451-474
[10] K. Liu, X. Ma, W. Zhang, Rigidity and Vanishing Theorems in K-theory. C.R. Acad. Sci., France, Serie I, 2000, 301-305
[11] K. Liu, Vanishing Theorems for Loop Spaces. AMS/IP Studies in Advanced Mathematics, 20, 2001, 311-317
[12] K. Liu, W. Zhang, Adiabatic Limits and Foliations. Contemporary Mathematics, 279, 2001, 195-208
[13] C.-C. Liu, K. Liu, J. Zhou, A proof of conjecture of Mari~no-Uafa on Hodge integrals. J. Diff. Geom., 65, 2003, 289-340
[14] K. Liu, X. Sun, S.-T. Yau, Canonical metrics on the moduli space of Riemann surfaces, I. J. Diff. Geometry, 68, 2004, 571-637
[15] K. Liu, X. Sun, S.-T. Yau, Canonical metrics on the moduli space of Riemann surfaces, II. J. Diff. Geometry, 69, 2005, 163-216
[16] C.C. Liu, K. Liu, J. Zhou, A formula of two-partition Hodge integrals. J. Amer. Math. Soc., 20, 2007, 149-184
[17] J. Li, M. Chiu-Chu, K. Liu, J. Zhou, A mathematical theory of the topological vertex. Geom. Topol., 13, 2009, 527-621
[18] K. Liu, H. Xu, Recursion formulae of higher Weil-Petersson volumes. Int. Math. Res. Not. IMRN, 2009, 835- 859
[19] K. Liu, H. Xu, A proof of the Faber intersection number conjecture. J. Diff. Geom., 83 (2), 2009, 313-335
[20] K. Liu, P. Peng, Proof of the Labastida-Marino-Ooguri-Vafa conjecture. J. Diff. Geom., 85(3), 2010, 479-525
[21] K. Liu, H. Xu, Computing Top intersections in the tautological ring of M-g. Math. Z., 270(3), 2012, 819- 837
[22] K. Liu, X. Yang, Curvature of direct image sheaves of vector bundles and applications. J. Diff. Geometry, 14, 2014, 117-145
[23] K. Liu, S. Rao, X. Yang, Quasi-isometry and deformations of Calabi-Yau manifolds. Invent. Math., 199, N.2, 2015, 423-453
[24] K. Liu, X. Yang, Effective vanishing theorems for ample and globally generated vector bundles. Comm. Anal. Geom., 23n4, 2015, 797-818
[25] H. Feng, K. Liu, X. Wan, Chern forms of holomorphic Finsler vector bundles and some applications. Internat. J. Math., 27n4, 2016, 1-22
[26] K. Liu, R. Vakil, H. Xu, Formal pseudodifferential operators and Witten's r-spin numbers. J. Reine Angew. Math., 728, 2017, 1-33
[27] K. Liu, Y. Shen, Boundedness of the period maps and global Torelli theorem. Sci. China Math., 60n6, 2017, 1029-1046
[28] F. Han, K. Liu, W. Zhang, Anomaly cancellation and modularity, II: the E88 case. Sci. China Math., 60n6, 2017, 985-994
[29] K. Liu, X. Yang, Ricci curvatures on Hermitian manifolds. Trans. Amer. Math. Soc., 369n7, 2017, 5157-5196
[30] H. Feng, K. Liu, X. Wan, A Donaldson type functional on a holomorphic Finsler vector bundle. Math. Ann., no. 3-4, 369, 2017, 997-1019
[31] K. Liu, H. Xu, F. Ye, E. Zhao, The extension and convergence of mean curvature ow in higher codimension. Trans. AMS, no. 3, 370, 2018, 2231-2262
[32] K. Liu, Y. Wu, On positive scalar curvature and moduli of curves. J. Diff. Geom., no. 2, 111, 2019, 315-328
联系方式 个人主页：http://www.math.ucla.edu/~liu/；E-mail：liu@math.ucla.edu