Kefeng Liu

Kefeng Liu

Kefeng Liu ( Chinese  劉克峰  /  刘克峰 , Pinyin Liú Kèfēng ; born December 12, 1965 in Kaifeng ) is a Chinese mathematician who studies algebraic geometry and topology, using methods from string theory.

Liu studied mathematics at the University of Beijing with a bachelor's degree in 1985, obtained a master's degree from the Chinese Academy of Sciences in 1988 and received his doctorate from Harvard University with Shing-Tung Yau in 1993 (Modular invariance and rigidity theorems). He was then a Moore Instructor at the Massachusetts Institute of Technology until 1996, was an Assistant Professor at Stanford University from 1996 , became an Associate Professor in 2000 and Professor at the University of California, Los Angeles (UCLA) in 2002 .

He is also a professor at Zhejiang University and executive director of its Center of Mathematical Sciences.

He was visiting scholar at the Chinese Academy of Sciences and visiting professor at the University of Science and Technology of China.

Liu was awarded the Morningside Medal for Studies on the Elliptical Gender by Edward Witten (Theorems of Rigidity and Its Disappearance Using The Theory of Modular Shapes, Kac-Moody Algebras, and Vertex Algebras ), Mirror Symmetry with Application to Curve Counting on Calabi -Yau manifolds and general projective manifolds with hypergeometric series and module spaces in algebraic geometry (calculation of the intersection numbers of the module spaces of flat connections on Riemann surfaces using cores of thermal conduction equations on Lie groups).

He proved that various theorems about the disappearance of anomalies in string theory can be derived from the theory of modular forms. With D. Kong he introduced the concept of the hyperbolic geometric flow. He proved the Marino- Vafa conjecture about Hodge integrals of modular spaces of Deligne-Mumford curves.

He was a Sloan Research Fellow in 1998 and a Guggenheim Fellow in 2002. In 1998 he received the Morningside Medal in silver and in 2004 in gold. In 2001 he was plenary speaker at the ICCM (International Congress of Chinese Mathematicians). In 2002 he was invited speaker at the International Congress of Mathematicians in Beijing (Mathematical results inspired by physics).

He is editor of Communications in Analysis and Geometry, one of the editors of Pure and Applied Mathematics Quarterly and Notices of the ICCM, and co-editor of the Asian Journal of Mathematics and the Pacific Journal of Mathematics.

Fonts

• On SL2 (Z) and topology, Math. Research Letter, 1 (1994), pp. 53-64.
• On Modular invariance and rigidity theorems, J. Diff. Geom. 41 (1995), pp. 343-396.
• Modular invariance and characteristic numbers, Comm. Math. Phys., 174 (1995), no. 1, pp. 29-42.
• with W. Zhang: Elliptic genus and -invariant, International Math. Res. Notices, no. 8 (1994), pp. 319-327. ${\displaystyle \eta }$
• Heat kernel and moduli space, part 1,2, Math. Res. Letter, 3 (1996), pp. 743-762, 4 (1997), pp. 569-588.
• Heat kernels, symplectic geometry, moduli spaces and finite groups, Surveys in differential geometry: differential geometry inspired by string theory, 1999, pp. 527-542
• with B. Lian, S.-T. Yau: Mirror principle, parts 1-4, Asian J. Math. 1 (1997), pp. 729-763; 3 (1999), pp. 109-146, pp. 771-800, Surveys in Differential Geometry 1999 (Part 4)
• with X. Ma, W. Zhang: On elliptic genera and foliations, Math. Res. Lett., 8 (2001), pp. 361-376
• with X. Ma: On family rigidity theorems I. Duke Math. J. 102 (2000), pp. 451-474.
• with X. Ma, J. Zhou, The elliptic genus of the Hilbert schemes of surfaces,
• with B. Lian, S.-T. Yau: A survey of the mirror principle, Montreal workshop on mirror symmetry and related topics 2000
• with C.-C. Liu , J. Zhou: A proof of the Marino-Vafa conjecture on Hodge integrals. J. Diff. Geom., 65 (2003), pp. 289-340

Web links

• Homepage at UCLA, with CV and overview of his scientific work

Individual evidence

1. ↑ Kefeng Liu in the Mathematics Genealogy Project (English)