Vertex Operator Algebras and Monstrous Moonshine

摘要：董先生将研究顶点算子代数和巨大的月光。将研究顶点算子代数、轨道理论、模函数和椭圆上同调之间的关系。主要研究者将确定各种模类别和构造顶点算子代数的归纳函子。康威-诺顿广义月光猜想有望成立。顶点算子代数是共形场论中的对称代数，共形场论是描述凝聚态物理中的二维临界现象和弦理论中弦的经典运动的重要物理理论。这是一项从代数领域开始的研究，但超越了它，涉及结不变量、量子群、可积系统、模形式、共形和拓扑场论。对这个项目的成功研究将导致新的数学发现，这在数学和物理学中都是重要的。

ABSTRACT, DONG The principal investigator will investigate vertex operator algebras and the monstrous moonshine. Relations among vertex operator algebras, orbifold theory, modular functions and elliptic cohomology will be studied. The principal investigator will determine various module categories and construct induction functor for vertex operator algebras. The Conway-Norton's generalized moonshine conjecture is expected to be established. Vertex operator algebras are symmetry algebras in conformal field theory which is an important physical theory describing both two-dimensional critical phenomena in condensed matter physics and classical motions of strings in string theory. This is a research that starts out in the field of algebra but moves beyond that to touch knot invariants, quantum groups, integrable systems, modular forms, and conformal and topological field theories. A successful study of this project will lead to new mathematical discoveries which will be important both in mathematics and physics.