Research Interest

• Algebraic Geometry

Recent Works

• Equivariant cohomology of incidence Hilbert schemes and
  loop algebras. Preprint. (with W.-P. Li)
  

Publication

• Integral cohomology of Hilbert schemes of points on surfaces.
  Commu. in Anal. and Geom. (to appear). (with W.-P. Li)
  
• On the crepancy of the Gieseker-Uhlenbeck morphism.
  Asian J. Math. 12 (2008), 213-224. (with Q. Zhang)
  
• Incidence Hilbert schemes and infinite dimensional Lie algebras.
  Procedings of the 4th International Congress of Chinese Mathematicians
  (HangZhou, 2007), 408-441, Vol II. (with W.-P. Li)
  
• The Gromov-Witten and Donaldson-Thomas correspondence
  for trivial elliptic fibrations.
  Internat. J. Math. 18 (2007), 821-838. (with D. Edidin)
  
• Hilbert schemes of points on the minimal resolution
  and soliton equations. Contemp. Math. 442 (2007), 435-462. (with W. Wang)
  
• On certain moduli spaces of ideal sheaves and Donaldson-Thomas
  invariants. Math. Res. Letters 14 (2007), 403-411.
  (with S. Katz and W.-P. Li)
  
• On the Euler numbers of certain moduli spaces of curves
  and points. Commu. in Anal. and Geom. 14 (2006), 387-410.
  (with W.-P. Li)
  
• Integral operators and integral cohomology classes of Hilbert
  schemes. Math. Ann. 331 (2005), 669-692. (with W. Wang)
  
• Hilbert scheme intersection numbers, Hurwitz numbers, and
  Gromov-Witten invariants. Contemp. Math. 392 (2005), 67-81.
  (with W.-P. Li and W. Wang)
  
• Hilbert schemes, integrable hierarchies,
  and Gromov-Witten theory.
  Intern. Math. Res. Notices 40 (2004), 2085-2104.
  (with W.-P. Li and W. Wang)
• The cohomology rings of Hilbert schemes via Jack polynomials.
  CRM Proceedings and Lecture Notes 38 (2004), 249-258.
  (with W.-P. Li and W. Wang)
• Ideals of the cohomology rings of Hilbert
  schemes and their applications.
  Transactions of the AMS 356 (2004), 245-265.
  (with W.-P. Li and W. Wang)
• Stable rank-2 bundles on Calabi-Yau manifolds.
  Internat. J. Math. 14 (2003), 1097-1120. (with W.-P. Li).
• Curves in the Hilbert schemes of points on surfaces.
  Contemp. Math. 322 (2003), 89-96. (with W.-P. Li and Q. Zhang).
• Stability of the cohomology rings of
  Hilbert schemes of points on surfaces.
  J. reine angew. Math. 554 (2003), 217-234.
  (with W.-P. Li and W. Wang)
• Gromov-Witten invariants of the Hilbert scheme
  of 3-points on P^2. Asian J. Math. 7 (2003), 551-574.
  (with D. Edidin and W.-P. Li)
• Hilbert schemes and W algebras.
  Intern. Math. Res. Notices 27 (2002), 1427--1456.
  (with W.-P. Li and W. Wang)
• Hilbert schemes and symmetric products: a dictionary.
  Contemp. Math. 310 (2002), 233-257. (with W. Wang)
• On 1-point Gromov-Witten invariants of
  the Hilbert schemes of points on surfaces.
  Proceedings of 8th G\" okova Geometry-Topology Conference.
  Turkish J. Math. 26 (2002), 53-68. (with W.-P. Li)
• Vertex algebras and the cohomology ring structure of
  Hilbert schemes of points on surfaces.
  Math. Ann. 324 (2002), 105-133. (with W.-P. Li and W. Wang)
• On blowup formulae for the $S$-duality conjecture of
  Vafa and Witten III: relations with vertex operator algebras.
  J. reine angew. Math. 542 (2002), 173-217. (with W.-P. Li).
• Generators for the cohomology ring of
  Hilbert schemes of points on surfaces.
  Intern. Math. Res. Notices 20 (2001), 1057-1074.
  (with W.-P. Li and W. Wang)
• Vector bundles, the $S$-duality conjecture of
  Vafa and Witten, and vertex algebras.
  Fitst International Congress of Chinese Mathematicians
  (Beijing, 1998), 235-240. AMS/IP Stud. Adv. Math. 20.
  Amer. Math. Soc., Providence, RI, 2001. (with W.-P. Li).
• On blowup formulae for the $S$-duality conjecture of Vafa and Witten.
  Invent. Math. 136 (1999), 451-482. (with W.-P. Li).
• Vertex operator algebras and the blowup formula
  for the $S$-duality conjecture of Vafa and Witten.
  Math. Res. Letters 5 (1998), 791-798. (with W.-P. Li).
• On blowup formulae for the $S$-duality conjecture of
  Vafa and Witten II: the universal functions.
  Math. Res. Letters 5 (1998), 439-453. (with W.-P. Li).
• Quantum cohomology of projective bundles over P^n.
  Transactions of the AMS 350 (1998), 3615-3638. (with Y. Ruan).
• Enumeration of nodal genus-2 plane curves with
  fixed complex structure. J. Alg. Geom. 7 (1998), 569-587.
  (with S. Katz and Y. Ruan).
• Extensions of vector bundles and rationality of
  certain moduli spaces of stable bundles.
  J. reine angew. Math. 475 (1996), 209-220. (with W.-P. Li).
• Rank-3 stable bundles on rational ruled surfaces.
  Math. Z. 222 (1996), 279-303. (with W.-P. Li).
• Flips of moduli spaces and transition formulas for
  Donaldson polynomial
  invariants of rational surfaces.
  Commu. in Anal. and Geom. 3 (1995), 11-83. (with R. Friedman).
• On complex surfaces diffeomorphic to rational surfaces.
  Invent. Math. 120 (1995), 81-117. (with R. Friedman).
• Stable vector bundles on algebraic surfaces.
  Transactions of AMS 345 (1994), 833-852. (with W.-P. Li).
• Complex structures on certain differentiable 4-manifolds.
  Topology 32 (1993), 551-566.
• Low-degree Donaldson polynomial invariants of rational surfaces.
  J. Alg. Geom. 2 (1993), 413-442. (with W.-P. Li)
• Equivalence classes of polarizations and moduli spaces of sheaves.
  J. Differ. Geom. 37 (1993), 397-415.
• On smooth structures of potential surfaces of general type
  homeomorphic to rational surfaces.
  Invent. Math. 113 (1993), 163-175.
• Moduli spaces of stable rank-2 bundles on ruled surfaces.
  Invent. Math. 110 (1992), 615-626.
• Simple sheaves versus stable sheaves on algebraic surfaces.
  Math. Z. 209 (1992), 559-579.
• Stable rank-$2$ bundles on simply connected elliptic surfaces.
  Duke Math. J. 67 (1992), 557-569.
• Birational properties of moduli spaces of stable locally free rank-2
  sheaves on algebraic surfaces. Manuscripta Math. 72 (1991), 163-180.
• Equivalence classes of polarizations and moduli spaces of rank two
  bundles on ruled surfaces. Columbia University Thesis, 1990.

Research Collaborators

• Dan Edidin
  
  • mailing address:
    Department of Mathematics
    University of Missouri
    Columbia, MO 65211
    U.S.A.
    
  • e-mail address:
    edidin@math.missouri.edu
• Robert Friedman
  
  • mailing address:
    Department of Mathematics
    Columbia University
    New York, NY 10027
    U.S.A.
    
  • e-mail address:
    rf@math.columbia.edu
• Sheldon Katz
  • mailing address:
    Department of Mathematics
    University of Illinois at Urbana-Champaign
    Urbana, IL 61801
    U.S.A.
    
  • e-mail address:
    katz@math.uiuc.edu
• Wei-Ping Li
  • mailing address:
    Department of Mathematics
    Hong Kong University of Science and Technology (HKUST)
    Clear Water Bay, Kowloon
    Hong Kong
    
    
    
  • e-mail address:
    mawpli@uxmail.ust.hk
  • Home Page of Wei-Ping Li
    
• Yongbing Ruan
  • mailing addresses:
    Department of Mathematics
    University of Michigan
    Ann Arbor, MI 48109-1043
    U.S.A.
    
  • e-mail addresses:
    ruan@umich.edu
    
• Weiqiang Wang
  • mailing address:
    Department of Mathematics
    University of Virginia
    Charlottesville, VA 22904-4137
    U.S.A.
    
  • e-mail address:
    ww9c@weyl.math.virginia.edu
  • Home Page of Weiqiang Wang
    
• Qi Zhang
  • mailing address:
    Department of Mathematics
    University of Missouri
    Columbia, MO 65211
    U.S.A.
    
  • e-mail address:
    qi@math.missouri.edu
    

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