Geometric Langlands Program and Beyond

几何朗兰兹纲领及其他

• 批准号: 0401164
• 负责人: Vladimir Drinfeld
• 金额: $ 68.59万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0401164&HistoricalAwards=false
• 关键词: Geometric; Langlands; Program; Beyond

DMS-0401164Vladimir Drinfeld, Alexander Beilinson, Dennis GaitsgoryThe principal investigators conduct research in the following areas: representation theory of Kac-Moody algebras, connections with arbitrary singularities on curves, moduli stacks of G-bundles on surfaces, representation theory of groups over two-dimensional fields, and geometric Langlands correspondence. They study representations of affine algebras at the critical level in terms of D-modules on natural varieties. They compute the determinant of the period isomorphism associated to a vector bundle V on a curve and a connection on V (which can have irregular singularities). They compactify the stack of G-bundles on a surface. They study the category of representations of groups over two-dimensional local fields on pro-vector spaces.The subject of the research lies on the intersection of several domains of modern mathematics - the Langlands program, representation theory, finite-dimensional and infinite-dimensional algebraic geometry. It will deepen our understanding of the Langlands program and possibly lead to its 2-dimensional generalization.

DMS-0401164弗拉基米尔·德林费尔德，亚历山大贝林森，丹尼斯Gaitsgory主要研究人员进行以下领域的研究：卡茨-穆迪代数的表示理论，曲线上任意奇点的连接，曲面上G-丛的模栈，二维域上群的表示理论，几何朗兰兹对应。他们研究表示的仿射代数在临界水平的D-模块的自然品种。 他们计算与曲线上的向量丛V和V上的联络（可以有不规则奇点）相关联的周期同构的行列式。 它们紧化了曲面上的G-丛。他们研究的类别表示的群体在二维局部领域的pro-vector spaces.The主题的研究在于交叉的几个领域的现代数学-朗兰兹计划，表示理论，有限维和无限维代数几何。这将加深我们对朗兰兹纲领的理解，并可能导致它的二维推广。