Conference Proposal: Talbot Workshops 2005 - 2007: Geometric Langlands

会议提案：Talbot 研讨会 2005 - 2007：几何朗兰兹

• 批准号: 0512714
• 负责人: Haynes Miller
• 金额: $ 3.83万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-03-15 至 2009-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0512714&HistoricalAwards=false
• 关键词: Conference; Proposal; Talbot; Workshops; 2005

AbstractAward: DMS-0512714Principal Investigator: Haynes R. Miller, Michael J. HopkinsThe Talbot program is a series of yearly workshop retreatsbringing together graduate students, recent PhDs, and facultymentors for an intense exploration of a topic of activemathematical research. The Talbot 2004 workshop was devoted tothe Stolz-Teichner model of elliptic cohomology and was mentoredby Stephan Stolz. The Talbot 2005 workshop will focus on thegeometric Langlands program and be mentored by David Ben-Zvi. Thegeometric Langlands program is one of the most fertile areas ofmathematics, integrating representation theory, topology, andalgebraic geometry. The original conjectures of Langlands tieinfinite-dimensional representation theory to the structure ofGalois groups, with profound applications to number theory. Fromthe geometric perspective deriving from the renowned theorem ofBorel-Weil-Bott, one would like to classify such representationsby equivariant sheaves on a parametrizing space. Drinfeld andLaumon, among others, adapted Langlands' original ideas forfunction fields to formulate a far reaching geometricgeneralization, now called the geometric Langlands program. Workin this area over the past twenty years has changed the face ofmodern representation theory. Recent advances, such as newgeometric generalizations of the classical Satake isomorphism,make this an ideal time to gather young mathematicians to studythese results, the techniques used to derive them, and newlyexposed avenues for future research.The Talbot workshops seek to introduce aspiring mathematicians toactive areas of mathematical research, foster community andcollaboration across subdisciplinary and institutional lines, andform pedagogical and research ties between establishedmathematicians and young researchers. The topic for Talbot 2004concerns a central problem in mathematics deeply related toneighboring areas of science. For instance, the crystallographicstudy of proteins, quantum states of particles, and the structureof integer solutions to polynomial equations are all central tochemistry, physics, and cryptography/number theory; their deeperstudy requires probing the algebraic structures that governaspects of their nature. Representation theory is precisely thefield of mathematics devoted to this study. Further, thegeometric Langlands program offers a unifying vision for thespecific algebraic structures suited to each of these areas,which are called reflection groups, Lie groups, and Galoisgroups. This Talbot workshop will bring together graduatestudents with different specialties and from many universities tospend a week focused on this important subject. The participantsand their mentor, David Ben-Zvi, will share a residence as wellas lectures, discussions, and meals. This informal atmosphere,mixing fellowship and intellectual interest, will promote aconcentrated study of the material and lay the foundation forfuture collaboration and research.

摘要：获奖：dms -0512714首席研究员：Haynes R. Miller, Michael J. hopkins Talbot项目是一系列的年度研讨会，汇集了研究生，最近的博士和教师导师，对一个活跃的数学研究主题进行深入的探索。Talbot 2004研讨会致力于研究椭圆上同调的Stolz- teichner模型，由Stephan Stolz指导。塔尔博特2005年研讨会将集中于几何朗兰兹程序，并由大卫本-兹维指导。几何朗兰兹程序是数学最丰富的领域之一，它集表示理论、拓扑学和代数几何于一体。朗兰兹的原始猜想将无限维表示理论与伽罗瓦群的结构联系在一起，对数论有着深远的应用。从著名的borel - weil - bott定理衍生出的几何角度来看，人们希望通过参数化空间上的等变束来对这种表示进行分类。德林菲尔德和劳蒙等人改编了朗兰兹关于函数场的原始思想，形成了一个影响深远的几何推广，现在被称为几何朗兰兹程序。在过去的二十年里，对这一领域的研究改变了现代表征理论的面貌。最近的进展，如经典竹同构的新几何推广，使得这是一个理想的时间来聚集年轻的数学家来研究这些结果，用于推导它们的技术，以及未来研究的新途径。Talbot研讨会旨在将有抱负的数学家引入活跃的数学研究领域，促进跨学科和机构线的社区和合作，并在成熟的数学家和年轻研究人员之间形成教学和研究联系。塔尔博特2004年的主题关注数学中的一个核心问题，该问题与邻近的科学领域密切相关。例如，蛋白质的晶体学研究、粒子的量子态和多项式方程的整数解的结构都是化学、物理和密码学/数论的核心；对它们进行更深入的研究，需要探究支配它们本质各方面的代数结构。表征理论正是致力于这一研究的数学领域。此外，几何朗兰兹程序为适合这些领域的特定代数结构提供了一个统一的愿景，这些结构被称为反射群、李群和伽罗isgroup。塔尔博特研讨会将汇集来自不同专业和多所大学的研究生，花一周时间专注于这一重要课题。参与者和他们的导师David Ben-Zvi将共享住所、讲座、讨论和用餐。这种非正式的氛围，混合了友谊和学术兴趣，将促进对材料的集中研究，并为未来的合作和研究奠定基础。