Mathematical Sciences: Riemann Surfaces and Analytic Torsion

约翰·费伊将对最近的发展进行研究 关于theta函数和黎曼曲面。这是一个领域 它的繁荣是因为它与 Kadomtsev-Petviashvili微分方程族和 弦理论。它也有很大的内在利益， 数学，因为它将有助于更高的理论 黎曼曲面上的秩向量丛 研究将集中在Ray-Singer解析挠率， 定义在黎曼向量丛的模空间上 表面。这将包括三个方面的研究。第一 关于全纯因子分解和消失性质 Jacobi簇上的挠率第二个涉及 挠率对模量的显式依赖关系的研究 Riemann曲面最后一个方面将涉及 广义Szego核和theta- 由秩二丛的挠率定义的函数。

John Fay will carry out research into recent developments relating theta functions and Riemann surfaces. This is an area which has flourished because of its connections with the Kadomtsev-Petviashvili hierarchy of differential equations and with string theory. It also has great intrinsic interest for mathematics since it will contribute towards a theory of higher rank vector bundles on Riemann surfaces. The research will center on Ray-Singer analytic torsion as defined on the moduli spaces of vector bundles on Riemann surfaces. This will include study of three aspects. The first concerns the holomorphic factorization and vanishing properties of torsion on the Jacobi variety. The second involves investigation of the explicit dependence of torsion on the moduli of the Riemann surface. The final aspect will be concerned with the properties of the generalized Szego kernel and theta- functions defined by torsion for rank-two bundles.