CHONGYING DONG Professor of Mathematics B.S. Xian Telecommunication & Engineering University, China. Ph.D. Academia Sinica, Beijing

Phone: 831-459-4642 Office: Baskin 365B Office Hours: By Appt. Email: dong_at_ucsc_dot_edu

RESEARCH INTERESTS

Vertex operator algebras are a new and fundamental class of algebraic structure which has recently arisen in mathematics and physics. This new algebra has beautiful connections with many directions in mathematics, such as the representation theory of the Virasoro algebra and affine Lie algebras, the theory of Riemann surfaces, knot invariants and invariants of three-dimensional manifolds, monodromy associated with differential equations, monster simple group and automorphic forms. The modern notion of chiral algebra in the physics literature essentially coincides with the notion of vertex operator algebra. From this point of view, the theory of vertex operator algebras and their representations form the algebraic foundation of conformal field theory.

Chongying Dong is interested in infinite-dimensional Lie algebras and their representations, vertex (operator) algebras and their representations, and conformal field theory. His recent research centers on three different directions: (1) The structure and the representations of vertex operator algebras. He works on both concrete examples and general theory. The generators and relations, automorphism groups and irreducible modules for well-known vertex operator algebras are investigated. He is also interested in the dual pairs and the reciprocity law, radicals in the theory of vertex operator algebras and classifications of certain class of vertex operator algebras. (2) Orbifold theory. Orbifold theory studies a vertex operator algebra with a finite automorphism group. The main problem is to determine the module category for the fixed point vertex operator sub-algebras. This problem is deeply related to the quantum doubles and elliptic cohomology. (3) Generalized moonshine. The generalized moon-shine is about the connection between the monster simple group and modular functions. The generalized moonshine conjectures says for any pair of commuting elements in the monster, one can associate a modular function of genus zero with additional properties. Solving this conjecture is one of Professor Dong's top priorities.

SELECTED PUBLICATIONS

C. Dong and K. Nagatomo: Classification of irreducible modules for the vertex operator algebra V+L for rank 1 lattice L, Comm. Math. Phys. 202, (1999), 169-195.

C. Dong, R. Griess, Jr. and G. Hoehn: Framed vertex operator algebras, codes and the moonshine module, Comm. Math. Phys. 193 (1998), 407-448.

C. Dong, H. Li and G. Mason: Twisted representations of vertex operator algebras, Math. Ann. 310 (1998), 571-600.

C. Dong, H. Li and G. Mason: Regularity of rational vertex operator algebras, Advances in Math. 132 (1997), 148-166.

C. Dong and G. Mason: On quantum Galois theory, Duke Math. J. 86 (1997), 305-321.

C. Dong, H. Li and G. Mason: Compact automorphism groups of vertex operator algebras, International Math. Research Notices 18 (1996), 913-921.

C. Dong: Representations of the moonshine module vertex operator algebra, Contemporary Math 175 (1994),
27-36.

C. Dong and J. Lepowsky: Generalized vertex algebras and relative vertex operators, Progress in Math. Vol. 112, Birkhauser, Boston, 1993.

C. Dong: Vertex algebras associated with even lattices, it
J. Algebra 160 (1993), 245-265.

return to top