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Documents  Mirkovic, Ivan | enregistrements trouvés : 5

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Research talks;Algebraic and Complex Geometry;Mathematical Physics

Kapustin and Witten introduced a powerful perspective on the geometric Langlands correspondence as an aspect of electric-magnetic duality in four dimensional gauge theory. While the familiar (de Rham) correspondence is best seen as a statement in conformal field theory, much of the structure can be seen in the simpler (Betti) setting of topological field theory using Lurie's proof of the Cobordism Hypothesis. In these lectures I will explain this perspective and illustrate its applications to representation theory following joint work with Nadler as well as Brochier, Gunningham, Jordan and Preygel. Kapustin and Witten introduced a powerful perspective on the geometric Langlands correspondence as an aspect of electric-magnetic duality in four dimensional gauge theory. While the familiar (de Rham) correspondence is best seen as a statement in conformal field theory, much of the structure can be seen in the simpler (Betti) setting of topological field theory using Lurie's proof of the Cobordism Hypothesis. In these lectures I will explain ...

14D24 ; 22E57 ; 22E46 ; 20G05

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Research talks;Algebra;Algebraic and Complex Geometry

We will report on an ongoing project to understand geometric Langlands in genus one, in particular a version that depends only on the topology of the curve (as appears in physical descriptions of the subject). The emphasis will be on the realization of the automorphic and spectral categories as the center/cocenter of the affine Hecke category. We will mention work with D. Ben-Zvi and A. Preygel that accomplishes this on the spectral side, then focus on ongoing work with D. Ben-Zvi, building on work with P. Li, that we expect will lead to a parallel automorphic result. We will report on an ongoing project to understand geometric Langlands in genus one, in particular a version that depends only on the topology of the curve (as appears in physical descriptions of the subject). The emphasis will be on the realization of the automorphic and spectral categories as the center/cocenter of the affine Hecke category. We will mention work with D. Ben-Zvi and A. Preygel that accomplishes this on the spectral side, then ...

22E57 ; 14D24

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Research talks;Algebra;Algebraic and Complex Geometry

We will discuss the problem of Langlands duality for the principal series category (alias: D-modules on the semi-infinite flag variety). In particular, we will explain how to relate Whittaker invariants to local systems for the Langlands dual group. This work can be understood as a chiralization of the Arkhipov-Bezrukavnikov theory.

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Research talks;Algebra;Algebraic and Complex Geometry

The loop Grassmannians of reductive groups will be reconsidered as a construction in the setting of “local spaces” over a curve. The notion of a local space is a version of the fundamental structure of a factorization space introduced and developed by Beilinson and Drinfeld. The weakening of the requirements formalizes some well-known examples of “almost factorization spaces.” The change of emphases leads to new constructions. The main example will be generalizations of loop Grassmannians corresponding to quadratic forms Q on based lattices. The quadratic form corresponding to the loop Grassmannian of a simply connected group G is the basic level of G. The loop Grassmannians of reductive groups will be reconsidered as a construction in the setting of “local spaces” over a curve. The notion of a local space is a version of the fundamental structure of a factorization space introduced and developed by Beilinson and Drinfeld. The weakening of the requirements formalizes some well-known examples of “almost factorization spaces.” The change of emphases leads to new constructions. The main example ...

14Mxx ; 14M15 ; 22E67

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Research talks;Algebraic and Complex Geometry;Mathematical Physics

Kapustin and Witten introduced a powerful perspective on the geometric Langlands correspondence as an aspect of electric-magnetic duality in four dimensional gauge theory. While the familiar (de Rham) correspondence is best seen as a statement in conformal field theory, much of the structure can be seen in the simpler (Betti) setting of topological field theory using Lurie's proof of the Cobordism Hypothesis. In these lectures I will explain this perspective and illustrate its applications to representation theory following joint work with Nadler as well as Brochier, Gunningham, Jordan and Preygel. Kapustin and Witten introduced a powerful perspective on the geometric Langlands correspondence as an aspect of electric-magnetic duality in four dimensional gauge theory. While the familiar (de Rham) correspondence is best seen as a statement in conformal field theory, much of the structure can be seen in the simpler (Betti) setting of topological field theory using Lurie's proof of the Cobordism Hypothesis. In these lectures I will explain ...

14D24 ; 22E57 ; 22E46 ; 20G05

... Lire [+]

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