# Regular Faculty

**Title**- Distinguished Professor

**Division**Physical & Biological Sciences**Department**- Mathematics Department

**Phone**831-459-4642**Email****Fax**831-459-4511**Website****Office Location**- McHenry Library, McHenry Building Room 4186

**Mail Stop**Mathematics Department**Mailing Address**- 1156 High Street
- Santa Cruz CA 95064

**Faculty Areas of Expertise**Mathematics

### 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

representation theory of vertex operator algebras. The main goal is to classify the rational vertex operator algebras and the irreducible representations. (2) Orbifold theory and generalized moonshine. 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 subalgebras and relevant trace functions. (3) Vertex operator algebras and conformal nets. There are a number of quite distinct approaches to conformal field theory in mathematics. The algebraic approach uses vertex operator algebras while the analytic approach uses conformal nets. The connection between algebraic and analytic approaches will be the central problem in this direction.

### Biography, Education and Training

B.S. Xian Telecommunication & Engineering University, China.

Ph.D. Academia Sinica, Beijing

### Selected Publications

- C. Dong and N. Yu, Z-graded weak modules and regularity, Comm. Math. Phys. 316 (2012), 269-277.
- C. Dong, R. Griess Jr. and C. Lam, Uniqueness results of the moonshine vertex operator algebra, American Journal of Math. 129 (2007), 583-609.
- C. Dong, H. Li and G. Mason, Modular invariance of trace functions in orbifold theory and generalized moonshine, Comm. Math. Phys. 214 (2000), 1-56.
- C. Dong, H. Li and G. Mason: Twisted representations of vertex operator algebras, Ma th. Ann. 310 (1998), 571-600.
- C. Dong, R. Griess, Jr. and G. Hoehn: Framed vertex operator algebras, codes and the moonshine module, Comm. Math. Phys. 193 (1998), 407-448.