受物理学启发的数学结果
Mathematical results inspired by physics
摘要：
我将讨论几何和拓扑学中三种不同类型的结果。(1)利用模形式、Kac-Moody代数和顶点算子代数证明了椭圆亏格的一般消失定理和刚性定理。(2)利用热核计算黎曼曲面上平坦联络的模空间的相交数。(3)利用超几何级数证明了Calabi-Yau流形和一般射影流形中计数曲线的镜像原理。
英文摘要：
I will discuss results of three different types in geometry and topology. (1) General vanishing and rigidity theorems of elliptic genera proved by using modular forms, Kac-Moody algebras and vertex operator algebras. (2) The computations of intersection numbers of the moduli spaces of flat connections on a Riemann surface by using heat kernels. (3) The mirror principle about counting curves in Calabi-Yau and general projective manifolds by using hypergeometric series.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
