Publications
Papers and Research Monographs
- Ernst equation with cosmological constant, with Xu Chongming,
Journal of Changsha Railway Institute 4 (1986), 1--3.
- Bäcklund theorems in 3-dimensional Minkowski space and their
higher-dimensional generalization, Acta Mathematica Sinica
29 (1986), 684--690.
- Global Bäcklund transformations in 3-dimensional Minkowski
space, unpublished, 17 pages.
- On the geometric interpretation of vertex operator algebras,
Ph.D. thesis, Rutgers University, 1990, 131 pages.
- Geometric interpretation of vertex operator algebras,
Proc.
Natl. Acad. Sci. USA 88 (1991), 9964--9968.
- 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.
- 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.
- Vertex operator algebras and conformal field theory,
International Journal of Modern Physics A 7 (1992),
2109--2151.
- 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.
- 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.
- 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.
- 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.
- 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.
- Operadic formulation of topological vertex algebras and
Gerstenhaber or
Batalin-Vilkovisky algebras,
Comm. in Math. Phys. 164 (1994), 105--144.
- A theory of tensor products for module categories for a vertex
operator
algebra, I, with J. Lepowsky, Selecta Mathematica 1
(1995), 699-756.
- A theory of tensor products for module categories for a vertex
operator
algebra, II, with J. Lepowsky, Selecta Mathematica 1
(1995), 757--786.
- 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.
- 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.
- A theory of tensor products for module categories for a vertex
operator
algebra, IV, J. Pure Appl. Alg. 100
(1995), 173--216.
- Introduction to vertex operator algebras, III, in:
Moonshine and vertex operator algebras, RIMS Kokyuroku 904,
RIMS, Kyoto, Japan, 1995, 51--77.
- 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.
- Virasoro vertex operator algebras,
(nonmeromorphic) operator product expansion and the tensor product
theory, J. Alg. 182 (1996), 201--234.
- 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.
- 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.
-
Two-dimensional conformal geometry and vertex operator algebras,
Progress in Mathematics, Vol. 148, 1997,
Birkhäuser, Boston, 280 pages.
-
Genus-zero modular functors and intertwining operator
algebras, Internat. J. Math. 9 (1998), 845--863.
- Intertwining operator algebras and vertex tensor categories for
affine Lie algebras, with
J. Lepowsky, Duke Math. J. 99 (1999), 113--134.
pdf file
-
A functional-analytic theory of vertex (operator) algebras, I,
Comm. Math. Phys. 204 (1999), 61--84.
pdf file
-
Generalized rationality and a Jacobi identity for
intertwining operator algebras, Selecta Math. 6 (2000),
225--267.
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Semi-infinite forms and topological vertex operator algebras>,
with W. Zhao, Comm. Contemp. Math.,
2 (2000), 191--241.
-
Factorization of formal exponential and uniformization, with
K. Barron and J. Lepowsky, J. Alg.
228 (2000), 551--579.
pdf file
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Vertex operators, with J. Lepowsky, article in:
Encyclopaedia of Mathematics, Supplement III, ed. by M. Hazewinkel,
Kluwer Academic Publishers, 2001.
-
Vertex operator algebras, with J. Lepowsky,
article in: Encyclopaedia of Mathematics, Supplement III, ed. by
M. Hazewinkel, Kluwer Academic Publishers, 2001.
-
Intertwining operator algebras and vertex tensor categories for
superconformal algebras, I, with A. Milas,
Comm. Contemp. Math. 4 (2002), 327--355.
-
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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Review of Vertex Algebras and Algebraic Curves by E. Frenkel and
D. Ben-Zvi, Bull. Amer. Math. Soc. 39 (2002),
585--591.
pdf file ps file
- 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.
pdf file ps file
- A functional-analytic theory of vertex (operator) algebras, II,
Comm. Math. Phys. 242 (2003), 425--444.
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- 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.
pdf file ps file
- 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.
pdf file ps file
- Open-string vertex algebras, tensor categories and operads,
with L. Kong, Comm. Math. Phys. 250 (2004), 433--471.
pdf file ps file
- Vertex operator algebras, the Verlinde conjecture and
modular tensor categories, Proc.
Natl. Acad. Sci. USA 102 (2005), 5352--5356.
pdf file ps file
(A
commentary on this paper by J. Lepowsky has also appeared in
the same issue.)
- Differential equations and intertwining operators,
Comm. Contemp. Math. 7 (2005), 375--400.
pdf file ps file
- Differential equations, duality and modular invariance,
Comm. Contemp. Math. 7 (2005), 649--706.
pdf file ps file
- 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.
pdf file ps file
- 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.
pdf file ps file
- 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.
pdf file ps file
- Full field algebras, with L. Kong, Comm. Math. Phys.
272 (2007), 345--396.
pdf file ps file
- 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.
pdf file ps file
- Vertex operator algebras and the Verlinde conjecture,
Comm. Contemp. Math. 10 (2008), 103--154.
pdf file ps file
- Rigidity and modularity of vertex tensor categories,
Comm. Contemp. Math. 10 (2008), 871--911.
pdf file ps file
- Cofiniteness conditions, projective covers and
the logarithmic tensor product theory, J. Pure
Appl. Alg. 213 (2009), 458--475.
pdf file ps file
- 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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- Modular invariance for conformal full field algebras,
with L. Kong, Trans. Amer. Math. Soc. 362 (2010), 3027--3067.
pdf file ps file
- Generalized twisted modules associated to general automorphisms
of a vertex operator algebra, Comm. Math. Phys. 298
(2010), 265--292.
pdf file
- Logarithmic intertwining operators and associative
algebras, with J. Yang, 38 pages, J. Pure
Appl. Alg., to appear.
pdf file
- A cohomology theory of grading-restricted
vertex algebras, 38 pages, to appear.
pdf file
- First and second cohomologies
of grading-restricted vertex algebras, 24 pages, to appear.
pdf file
- Logarithmic
tensor category theory for generalized modules for a conformal
vertex algebra, I: Introduction and strongly graded
algebras and their generalized modules, with J, Lepowsky and L. Zhang,
81 pages, to appear.
pdf file
- Logarithmic
tensor category theory, II: Logarithmic formal calculus
and properties of logarithmic intertwining operators, with J, Lepowsky
and L. Zhang, 40 pages, to appear.
pdf file
- Logarithmic
tensor category theory, III: Intertwining maps and tensor
product bifunctors, with J, Lepowsky and L. Zhang, 36 pages, to appear.
pdf file
- Logarithmic
tensor category theory, IV: Constructions of tensor
product bifunctors and the compatibility conditions, with J, Lepowsky
and L. Zhang, 94 pages, to appear.
pdf file
- Logarithmic
tensor category theory, V: Convergence condition for
intertwining maps and the corresponding compatibility
condition, with J, Lepowsky and L. Zhang, 50 pages, to appear.
pdf file
- Logarithmic
tensor category theory, VI: Expansion condition, associativity of
logarithmic
intertwining operators, and the associativity isomorphisms, with J,
Lepowsky and L. Zhang, 108 pages,
to appear.
pdf file
- Logarithmic
tensor category theory, VII: Convergence and extension
properties and applications to expansion for intertwining
maps, with J, Lepowsky and L. Zhang, 20 pages,
to appear.
pdf file
- Logarithmic
tensor category theory, VIII: Braided tensor category
structure on categories of generalized modules for a
conformal vertex algebra, with J, Lepowsky and L. Zhang, 36 pages,
to appear.
pdf file
- Eigenfunctions on a Riemannian manifold and representations of
a vertex operator algebra, 32 pages, to appear.
- A theory of tensor products for module categories
for a vertex operator algebra, V, with J. Lepowsky, 50 pages, to
appear.
- Braided tensor categories and extensions of vertex operator
algebras, with A. Kirillov, Jr. and J. Lepowsky, 20 pages,
to appear.
- A construction of conformal intertwining
algebras, in preparation.
- Intertwining algebras, in preparation.
Books Edited
-
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.
-
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.
- 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.
Notes of lectures and talks
- Lecture notes at Joint Mathematics and Physics summer
school on Topological phases, conformal field theory and
tensor category, June 28 - July 2, 2010,
Institute for Advanced Study, Tsinghua University, Beijing, China.
pdf
file
- Notes of my talk at the workshop "Topological Phases and Emergent
Phenomena in Physics", July 5-9, 2010, Department of Physics,
Fudan University,
Shanghai, China.
pdf
file
- Lecture notes for my course ``Introduction to representation
theory and tensor categories", March to June, 2011, Beijing
International Center for Mathematical Research, Peking University,
Beijing, China.
pdf
file (These notes will be updated offen.)
- Slides for my talk "Quantum Hall states and the representation theory of
vertex operator algebras", November 18, 2011, CUNY Representation Theory Seminar,
Graudate Center, CUNY, New York.
pdf
file
- Slides for my talk "Quantum Hall states and the representation theory of
vertex operator algebras", January 9, 2012, Academy of Mathematics and
Systems Science, Chinese
Academy of Sciences, Beijing, China.
pdf
file
- Slides for my talk "Eigenfunctions on a Riemannian manifold and
representations of a vertex operator algebra" at the workshop
Mathematical Foundations of Quantum Field Theory, January 16 - 20, 2012,
Simon Center for Geometry and Physics, State University of New York
at Stony Brook, Stony Brook, New York.
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file
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