Problems in arithmetic groups and multiple Dirichlet series.
算术群和多重狄利克雷级数问题。
基本信息
- 批准号:1101640
- 负责人:
- 金额:$ 15.59万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2011
- 资助国家:美国
- 起止时间:2011-07-01 至 2016-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This project focuses on problems in arithmetic groups and multiple Dirichlet series, problems that are intimately related to automorphic forms. One part addresses topics related to cohomology of arithmetic groups and allied areas, such as the geometry of locally symmetric spaces and the conjectures linking cohomology to arithmetic geometry and Galois representations. The second part studies multiple Dirichlet series attached to Weyl groups, affine Weyl groups, and principal homogeneous vector spaces, and their connections to combinatorics, representation theory, automorphic forms, and mathematical physics. As writing projects, the principal investigator will continue to work with F. Hirzebruch and D. Zagier on updating their book "The Atiyah-Singer theorem and elementary number theory." He will also work with W. Stein to prepare a revised version of "Modular forms, a computational approach."This proposal deals with the interactions between number theory and representation theory. Number theory is the study of the properties of the whole numbers, and is the oldest branch of mathematics. Representation theory is the systematic study of symmetry, through the development of simple mathematical objects that encode the fundamental irreducible pieces of symmetry. A principal aim of the proposal is to explore relationships between these two subjects in the spirit of the "Langlands philosophy," which predicts deep connections between number theory and representation theory. Today the questions and phenomena addressed by these subjects serve as driving forces in much of contemporary mathematics research. Moreover, the subjects have contributed many applications in such diverse areas as codes and data transmission, chemistry, physics, and theoretical computer science.
这个项目的重点是算术群和多重狄利克雷级数的问题,这些问题与自守形式密切相关。 第一部分涉及与算术群和相关领域的上同调相关的主题,如局部对称空间的几何和将上同调与算术几何和伽罗瓦表示联系起来的结构。 第二部分研究附在Weyl群、仿射Weyl群和主齐次向量空间上的多重狄利克雷级数,以及它们与组合学、表示论、自守形式和数学物理的联系。 作为写作项目,主要研究者将继续与F。Hirzebruch和D. Zagier在更新他们的书“Atiyah-Singer定理和初等数论。”他还将与W。斯坦因编写的修订版“模块形式,一种计算方法。“这个提议涉及数论和表示论之间的相互作用。 数论是研究整数的性质,是数学最古老的分支。表示论是对称性的系统研究,通过发展简单的数学对象来编码对称性的基本不可约部分。 该提案的主要目的是本着“朗兰兹哲学”的精神探索这两个学科之间的关系,该哲学预测了数论和表示论之间的深刻联系。 今天,这些学科所解决的问题和现象成为当代数学研究的驱动力。 此外,这些学科在编码和数据传输、化学、物理和理论计算机科学等不同领域都有许多应用。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Paul Gunnells其他文献
Paul Gunnells的其他文献
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{{ truncateString('Paul Gunnells', 18)}}的其他基金
Multiple Dirichlet series, Whittaker functions, and the cohomology of arithmetic groups
多重狄利克雷级数、惠特克函数和算术群的上同调
- 批准号:
1501832 - 财政年份:2015
- 资助金额:
$ 15.59万 - 项目类别:
Continuing Grant
EAGER: Braid Statistics and Hard Problems in Braid Groups with Applications to Cryptography
EAGER:辫子统计和辫子组中的难题及其在密码学中的应用
- 批准号:
1551271 - 财政年份:2015
- 资助金额:
$ 15.59万 - 项目类别:
Standard Grant
Problems in number theory and representation theory
数论和表示论中的问题
- 批准号:
0801214 - 财政年份:2008
- 资助金额:
$ 15.59万 - 项目类别:
Standard Grant
Number Theory, Algebraic Geometry & Representation Theory
数论、代数几何
- 批准号:
0401525 - 财政年份:2004
- 资助金额:
$ 15.59万 - 项目类别:
Standard Grant
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