Dr. Zhenbo Qin’s research career began with the study of moduli spaces of sheaves and its application to Donaldson theory. In 1991, he answered a question raised by F. Hirzebruch in 1954. In 1994, together with R. Friedman, he proved the smooth invariance of the Kodaira dimension of complex surfaces, settling a conjecture of A. Van de Ven and also solved a classical problem dating back to the Italian School of algebraic geometers around the beginning of the 20th century. In 1999, together with W.-P. Li, he verified the blow-up formula for the S-duality conjecture of C. Vafa-E. Witten. In another joint work with W.-P. Li , he obtained the structure of the genus-0 extremal Gromov-Witten invariants of the Hilbert schemes of points on complex surfaces, confirming Y. Ruan’s Cohomological Crepant Resolution Conjecture for these Hilbert schemes in 2012.
Dr. Qin’s research has been supported by National Science Foundation, National Security Agency, American Institute of Mathematics, and Simons Foundation. He was the recipient of the Junior Faculty Enhancement Award (Oak Ridge Associated Universities, 1994-1995), the Alfred P. Sloan Research Fellow (Alfred P. Sloan Foundation, 1997-2001), and the Chancellor’s Award for Outstanding Research and Creative Activity (Physical and Mathematical Sciences, 2004). From 2007 to 2012, Dr. Qin was the Leonard M. Blumenthal Distinguished Professor in Department of Mathematics.
1990 Ph.D., Columbia University, Mathematics
1989 M.Phil., Columbia University, Mathematics
1987 M.S., Columbia University, Mathematics
1986 Diploma in English, Beijing Foreign Languages Institute
1985 B.S., Wuhan University, China, Mathematics
Frequently Taught Courses
MATH 2300 Calculus III
MATH 4100 Differential Equations
MATH 8210 Basic Algebra
MATH 8615 Algebraic Geometry
Dr. Zhenbo Qin’s research is in Algebraic Geometry, focusing on the study of moduli spaces such as the moduli spaces of sheaves and the moduli spaces of stable maps. Applications to gauge theory and string theory in physics include Donaldson theory, Gromov-Witten theory and Donaldson-Thomas theory.
authored by Zhenbo Qin
reviewed by Zhenbo Qin
Wei-Ping Li, Zhenbo Qin: Donaldson-Thomas invariants of certain Calabi-Yau 3-folds. Communications in Analysis and Geometry 21 (2013), 541-578.
Sheldon Katz, Wei-Ping Li, Zhenbo Qin: On certain moduli spaces of ideal sheaves and Donaldson-Thomas invariants. Math. Res. Letters 14 (2007), 403-411.
Wei-Ping Li, Zhenbo Qin, Weiqiang Wang: Vertex algebras and the cohomology ring structure of Hilbert schemes of points on surfaces. Math. Ann. 324 (2002), 105-133.
Wei-Ping Li, Zhenbo Qin: On blowup formulae for the S-duality conjecture of Vafa and Witten. Invent. Math. 136 (1999), 451-482.
Robert Friedman, Zhenbo Qin: On complex surfaces diffeomorphic to rational surfaces. Invent. Math. 120 (1995), 81-117.
Zhenbo Qin: Equivalence classes of polarizations and moduli spaces of sheaves. J. Differ. Geom. 37 (1993), 397-415.
Zhenbo Qin: Complex structures on certain differentiable 4-manifolds. Topology 32 (1993),551-566.