课题基金 / 基金详情

Mathematical Sciences: New Models in the Rankin-Selberg Method and Uses of the Metaplectic Group

Mathematical Sciences: New Models in the Rankin-Selberg Method and Uses of the Metaplectic Group
数学科学:Rankin-Selberg 方法的新模型和 Metaplectic 群的使用
批准号:
9023441
负责人:
Daniel Bump
金额:
$21.71万
依托单位:
依托单位国家:
美国
项目类别:
Continuing Grant
财政年份:
1991
资助国家:
美国
项目状态:
已结题
起止时间:
1991-07-15 至 1997-12-31

项目摘要

项目成果

Daniel Bump的其他基金

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中文摘要
翻译
该奖项支持D. Bump教授在自同构函数方面的研究。他打算扩展Rankin Selberg方法,并研究元塑群的新用途。这些包括对GL(2) n-fold盖上的函数的非唯一Whittaker模型的研究。模形式起源于19世纪中期的非欧几里得几何。因此,数学家和物理学家很早就认识到,许多具有根本重要性的物体在其基本性质上是非欧几里得的。这个领域主要关注关于整数的问题,但在使用几何和分析时,它保留了与历史根源的联系,因此与理论物理中的规范理论和信息论中的编码理论等领域的问题联系在一起。
英文摘要
This award supports the research of Professor D. Bump to work in automorphic functions. He intends to work on extending the Rankin Selberg method and on new uses of the metaplectic group. These include the study of non-unique Whittaker models of theta functions on the n-fold cover of GL(2). Modular forms arose out of Non-Euclidean geometry in the middle of the nineteenth century. Both mathematicians and physicists have thus long realized that many objects of fundamental importance are non-Euclidean in their basic nature. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots and thus to problems in areas as diverse as gauge theory in theoretical physics and coding theory in information theory.
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Conference Proposal: Automorphic Forms on Reductive Groups and Their Covers
  • 批准号:
    1802887
  • 项目类别:
    Standard Grant
  • 资助金额:
    $1.5万
  • 财政年份:
    2018
  • 负责人:
    Daniel Bump
  • 依托单位:
Unique Functionals and Quantum Groups
  • 批准号:
    1601026
  • 项目类别:
    Continuing Grant
  • 资助金额:
    $19.0万
  • 财政年份:
    2016
  • 负责人:
    Daniel Bump
  • 依托单位:
Collaborative Research: SI2-SSE: Sage-Combinat: Developing and Sharing Open Source Software for Algebraic Combinatorics
  • 批准号:
    1147463
  • 项目类别:
    Standard Grant
  • 资助金额:
    $14.37万
  • 财政年份:
    2012
  • 负责人:
    Daniel Bump
  • 依托单位:
Metaplectic Whittaker functions and quantum groups
  • 批准号:
    1001079
  • 项目类别:
    Standard Grant
  • 资助金额:
    $29.99万
  • 财政年份:
    2010
  • 负责人:
    Daniel Bump
  • 依托单位:
国内基金
海外基金
Handbook of the Mathematics of the Arts and Sciences的中文翻译
  • 批准号:
    12226504
  • 项目类别:
    数学天元基金项目
  • 资助金额:
    20.0万元
  • 批准年份:
    2022
  • 负责人:
    黄朝凌
  • 依托单位:
SCIENCE CHINA: Earth Sciences
Journal of Environmental Sciences
SCIENCE CHINA Information Sciences