Geometric Langlands Program and Beyond

点击翻译按钮获取中文摘要

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.