Publications

Papers and Research Monographs

1. Ernst equation with cosmological constant, with Xu Chongming, Journal of Changsha Railway Institute 4 (1986), 1--3.

2. Bäcklund theorems in 3-dimensional Minkowski space and their higher-dimensional generalization, Acta Mathematica Sinica 29 (1986), 684--690.

3. Global Bäcklund transformations in 3-dimensional Minkowski space, unpublished, 17 pages.

4. On the geometric interpretation of vertex operator algebras, Ph.D. thesis, Rutgers University, 1990, 131 pages.

5. Geometric interpretation of vertex operator algebras, Proc. Natl. Acad. Sci. USA 88 (1991), 9964--9968.

6. Toward a theory of tensor product for representations of a vertex operator algebra, with J. Lepowsky, in Proc. 20th Intl. Conference on Diff. Geom. Methods in Theoretical Physics, New York, 1991, ed. S. Catto and A. Rocha, World Scientific, Singapore, 1992, Vol. 1, 344--354.

7. Applications of the geometric interpretation of vertex operator algebras, in Proc. 20th Intl. Conference on Diff. Geom. Methods in Theoretical Physics, New York, 1991, ed. S. Catto and A. Rocha, World Scientific, Singapore, 1992, Vol. 1, 333--343.

8. Vertex operator algebras and conformal field theory, International Journal of Modern Physics A 7 (1992), 2109--2151.

9. On axiomatic approaches to vertex operator algebras and Modules, with I.B. Frenkel and J. Lepowsky, Memoirs Amer. Math. Soc. 104, No. 494 (1993), American Mathematical Society, Providence, 64 pages.

10. Vertex operator algebras and operads, with J. Lepowsky, The Gelfand Mathematical Seminars, 1990--1992, ed. L. Corwin, I. Gelfand and J. Lepowsky, Birkhäuser, Boston, 1993, 145--161.

11. A theory of tensor products for module categories for a vertex operator algebra, I, with J. Lepowsky, in: Geometric aspects of infinite integrable systems, Kyoto, 1993, RIMS Kokyuroku 883, RIMS, Kyoto, Japan, 1994, 148--203.

12. Binary trees and finite-dimensional Lie algebras, in Proc. AMS Summer Research Institute on Algebraic Groups and Their Generalizations, Pennsylvania State University, 1991, ed. W. J. Haboush and B. J. Parshall, American Mathematical Society, Providence, 1994, Vol. 2, 337--348.

13. Operadic formulation of the notion of vertex operator algebra, with J. Lepowsky, in: Mathematical Aspects of Conformal and Topological Field Theories and Quantum Groups, Proc. Joint Summer Research Conference, Mount Holyoke, 1992, ed. P. Sally, M. Flato, J. Lepowsky, N. Reshetikhin and G. Zuckerman, Contemporary Math., Vol. 175, Amer. Math. Soc., Providence, 1994, 131--148.

14. Operadic formulation of topological vertex algebras and Gerstenhaber or Batalin-Vilkovisky algebras, Comm. in Math. Phys. 164 (1994), 105--144.

15. A theory of tensor products for module categories for a vertex operator algebra, I, with J. Lepowsky, Selecta Mathematica 1 (1995), 699-756.

16. A theory of tensor products for module categories for a vertex operator algebra, II, with J. Lepowsky, Selecta Mathematica 1 (1995), 757--786.

17. Tensor products of modules for a vertex operator algebra and vertex tensor categories, with J. Lepowsky, in: Lie Theory and Geometry, in honor of Bertram Kostant, ed. R. Brylinski, J.-L. Brylinski, V. Guillemin, V. Kac, Birkhäuser, Boston, 1994, 349--383.

18. A theory of tensor products for module categories for a vertex operator algebra, III, with J. Lepowsky, J. Pure Appl. Alg. 100 (1995), 141--171.

19. A theory of tensor products for module categories for a vertex operator algebra, IV, J. Pure Appl. Alg. 100 (1995), 173--216.

20. Introduction to vertex operator algebras, III, in: Moonshine and vertex operator algebras, RIMS Kokyuroku 904, RIMS, Kyoto, Japan, 1995, 51--77.

21. A nonmeromorphic extension of the moonshine module vertex operator algebra, in: Moonshine, the Monster and related topics, Proc. Joint Summer Research Conference, Mount Holyoke, 1994, ed. C. Dong and G. Mason, Contemporary Math., Vol. 193, Amer. Math. Soc., Providence, 1996, 123--148.

22. Virasoro vertex operator algebras, (nonmeromorphic) operator product expansion and the tensor product theory, J. Alg. 182 (1996), 201--234.

23. On the D-module and formal variable approaches to vertex algebras, with J. Lepowsky, in: Topics in Geometry: In Memory of Joseph D'Atri, ed. S. Gindikin, Progress in Nonlinear Differential Equations, Vol. 20, Birkhäuser, Boston, 1996, 175--202.

24. Intertwining operator algebras, genus-zero modular functors and genus-zero conformal field theories, in: Operads: Proceedings of Renaissance Conferences, ed. J.-L. Loday, J. Stasheff, and A. A. Voronov, Contemporary Math., Vol. 202, Amer. Math. Soc., Providence, 1997, 335--355.

25. Two-dimensional conformal geometry and vertex operator algebras, Progress in Mathematics, Vol. 148, 1997, Birkhäuser, Boston, 280 pages.

26. Genus-zero modular functors and intertwining operator algebras, Internat. J. Math. 9 (1998), 845--863.

27. Intertwining operator algebras and vertex tensor categories for affine Lie algebras, with J. Lepowsky, Duke Math. J. 99 (1999), 113--134.
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28. A functional-analytic theory of vertex (operator) algebras, I, Comm. Math. Phys. 204 (1999), 61--84.
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29. Generalized rationality and a Jacobi identity for intertwining operator algebras, Selecta Math. 6 (2000), 225--267.
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30. Semi-infinite forms and topological vertex operator algebras>, with W. Zhao, Comm. Contemp. Math., 2 (2000), 191--241.

31. Factorization of formal exponential and uniformization, with K. Barron and J. Lepowsky, J. Alg. 228 (2000), 551--579.
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32. Vertex operators, with J. Lepowsky, article in: Encyclopaedia of Mathematics, Supplement III, ed. by M. Hazewinkel, Kluwer Academic Publishers, 2001.

33. Vertex operator algebras, with J. Lepowsky, article in: Encyclopaedia of Mathematics, Supplement III, ed. by M. Hazewinkel, Kluwer Academic Publishers, 2001.

34. Intertwining operator algebras and vertex tensor categories for superconformal algebras, I, with A. Milas, Comm. Contemp. Math. 4 (2002), 327--355.

35. Intertwining operator algebras and vertex tensor categories for superconformal algebras, II, with A. Milas, Trans. Amer. Math. Soc. 354 (2002), 363--385.
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36. Review of Vertex Algebras and Algebraic Curves by E. Frenkel and D. Ben-Zvi, Bull. Amer. Math. Soc. 39 (2002), 585--591.
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37. Riemann surfaces with boundaries and the theory of vertex operator algebras, in: Vertex Operator Algebras in Mathematics and Physics, ed. S. Berman, Y. Billig, Y.-Z. Huang and J. Lepowsky, Fields Institute Communications, Vol. 39, Amer. Math. Soc., Providence, 2003, 109--125.
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38. A functional-analytic theory of vertex (operator) algebras, II, Comm. Math. Phys. 242 (2003), 425--444.
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39. Differential equations and conformal field theories, in: Nonlinear Evolution Equations and Dynamical Systems, Proc. ICM2002 Satellite Conference, Yellow Mountains, 2002, ed. by Y. Cheng, S. Hu, Y. Li and C. Peng, World Scientific, Singapore, 2003, 61--71.
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40. Conformal-field-theoretic analogues of codes and lattices, in: Kac-Moody Lie Algebras and Related Topics, Proc. Ramanujan International Symposium on Kac-Moody Lie algebras and applications, ed. N. Sthanumoorthy and K. C. Misra, Contemp. Math., Vol. 343, Amer. Math. Soc., Providence, 2004, 131--145.
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41. Open-string vertex algebras, tensor categories and operads, with L. Kong, Comm. Math. Phys. 250 (2004), 433--471.
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42. Vertex operator algebras, the Verlinde conjecture and modular tensor categories, Proc. Natl. Acad. Sci. USA 102 (2005), 5352--5356.
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    (A commentary on this paper by J. Lepowsky has also appeared in the same issue.)

43. Differential equations and intertwining operators, Comm. Contemp. Math. 7 (2005), 375--400.
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44. Differential equations, duality and modular invariance, Comm. Contemp. Math. 7 (2005), 649--706.
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45. On the concepts of intertwining operator and tensor product module in vertex operator algebra theory, with J. Lepowsky, H. Li and L. Zhang, Jour. Pure Appl. Alg. 204 (2005), 507--535.
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46. Vertex operator algebras, fusion rules and modular transformations, in: Non-commutative Geometry and Representation Theory in Mathematical Physics, ed. J. Fuchs, J. Mickelsson, G. Rozenblioum and A. Stolin, Contemporary Math. Vol. 391, Amer. Math. Soc., Providence, 2005, 135--148.
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47. A logarithmic generalization of tensor product theory for modules for a vertex operator algebra, with J. Lepowsky and L. Zhang, Internat. J. Math. 17 (2006), 975--1012.
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48. Full field algebras, with L. Kong, Comm. Math. Phys. 272 (2007), 345--396.
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49. An equivalence of two constructions of permutation-twisted modules for lattice vertex operator algebras, with K. Barron and J. Lepowsky, Jour. Pure Appl. Alg. 210 (2007), 797--826.
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50. Vertex operator algebras and the Verlinde conjecture, Comm. Contemp. Math. 10 (2008), 103--154.
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51. Rigidity and modularity of vertex tensor categories, Comm. Contemp. Math. 10 (2008), 871--911.
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52. Cofiniteness conditions, projective covers and the logarithmic tensor product theory, J. Pure Appl. Alg. 213 (2009), 458--475.
    DOI information: 10.1016/j.jpaa.2008.07.016.
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53. Representations of vertex operator algebras and braided finite tensor categories, in: Vertex Operator Algebras and Related Topics, An International Conference in Honor of Geoffery Mason's 60th Birthday, ed. M. Bergvelt, G. Yamskulna and W. Zhao, Contemporary Math., Vol. 497, Amer. Math. Soc., Providence, 2009, 97--111.
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54. Modular invariance for conformal full field algebras, with L. Kong, Trans. Amer. Math. Soc., 55 pages, to appear.
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55. Generalized twisted modules associated to general automorphisms of a vertex operator algebra, Comm. Math. Phys., 38 pages, to appear.
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56. Logarithmic tensor product theory for generalized modules for a conformal vertex algebra, with J. Lepowsky and Lin Zhang, 319 pages, to appear.
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57. A theory of tensor products for module categories for a vertex operator algebra, V, with J. Lepowsky, 50 pages, to appear.

58. Braided tensor categories and extensions of vertex operator algebras, with A. Kirillov, Jr. and J. Lepowsky, 20 pages, to appear.

59. A construction of conformal intertwining algebras, in preparation.

60. Intertwining algebras, in preparation.

Books Edited

1. Recent developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory, Proceedings of an International Conference on Infinite-Dimensional Lie Theory and Conformal Field Theory, Charlottesville, 2000, with S. Berman, P. Fendley, K. Misra and B. Parshall, Contemporary Mathematics, Vol. 297, Amer. Math. Soc., Providence, 2002.

2. Vertex Operator Algebras in Mathematics and Physics, with S. Berman, Y. Billig and J. Lepowsky, Fields Institute Communications, Vol. 39, Amer. Math. Soc., Providence, 2003.

3. Lie algebras, vertex operator algebras and their applications, Proceedings of a conference in honor of James Lepowsky and Robert Wilson, 2005, with K. Misra, Contemporary Mathematics, Vol. 442, Amer. Math. Soc., Providence, 2007.