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Content archived on 2022-12-23

D-Modules, quantum groups and moduli of vector bundles: arithmetic and geometry

Objective



The aim of the project is to study new problems of algebraic and analytic geometry with emphasis on D-modules and moduli spaces of G-bundles, as well as related problems of infinite-dimensional groups, quantum groups, and their applications.

The purpose is : to construct and study natural families of D-modules on G-bundles on a smooth projective curve and to clarify their relation to Langlands' program; to develop an algebraic-geometric formalism for operator product expansion in conformal field theory; to study geometric realisations of representations of quantum groups as D-modules on configuration spaces; to study homogeneous spaces of quantum groups and PoissonLie groups; and to study index formulae and integral transformations such as the Penrose transform using D-module theory.

Call for proposal

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Funding Scheme

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Coordinator

Centre National de la Recherche Scientifique
EU contribution
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Address
Place Jussieu 4
75252 Paris
France

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Total cost
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Participants (7)