Zeta Values and Infinite Dimensional Representations

教授布洛赫将研究zeta函数和无限维李代数和函数群的表示之间的关系。他将专注于与zeta和L系列，准模块化和相关的模块化属性扩展已知的模块化属性的字符在一个变量和镜像对称性的关系值的关系。 研究者还将尝试发现一个黎曼罗克定理的向量丛与平坦的联系，使用代数陈西蒙斯字符类。这是一个项目，在这两个表示论和几何。在数学中，一项研究会产生一个无限的数字序列，代表被研究对象的基本信息，这是一种常见的现象。 这样的序列看起来是随机形成的，尽管它实际上完全由它被识别的方式决定。 某些数学函数，zeta和L-级数，长期以来一直被认为包含了关于这些序列中数字分布的重要信息。 zeta和L-级数的重要例子通常与抽象数学结构、代数和群的具体表示有关。不幸的是，数学家们并不完全理解数列和这些级数之间的联系，或者级数和表示法之间的联系。 如果这两种联系都被正规化，数学将拥有一种强大的新发现方法。本项目将研究第二组这些连接。

Professor Bloch will study relations between zeta functions and representations of infinite dimensional Lie algebras and function groups. He will focus on relations with values of zeta and L-series, quasi-modularity and related modular properties extending known modular properties for characters in one variable and relations with mirror symmetries. The investigator will also attempt to discover a Riemann Roch theorem for vector bundles with flat connections, using algebraic Chern Simons character classes.This is a project in both representation theory and geometry. It is a common occurrence in mathematics that a investigation will produce an infinite sequence of numbers representing basic information about the objects under study. Such a sequence can appear to form quite randomly, even though it is actually completely determined by the way it was identified. Certain mathematical functions, zeta and L-series, have long been known to contain important information about the distribution of numbers in such sequences. Important examples of zeta and L-series are often connected to the concrete representations of the abstract mathematical constructions, algebras and groups. Unfortunately, mathematicians do not fully understand either the connection between number sequences and these series or the connection between the series and the representations. If both of these connections were regularized, mathematics would have a powerful new method of discovery. This project will investigate the second set of these connections.