Gauge theory, ramification, and the geometric Langlands program
نویسندگان
چکیده
منابع مشابه
Gauge Theory and the Geometric Langlands Program
The Langlands program of number theory, or what we might call Langlands duality, was proposed in more or less its present form by Robert Langlands, in the late 1960s. It is a kind of unified scheme for many results in number theory ranging from quadratic reciprocity, which is hundreds of years old, to modern results such as Andrew Wiles’ proof of Fermat’s last theorem, which involved a sort of ...
متن کاملGauge Theory and Langlands Duality
In the late 1960s Robert Langlands launched what has become known as the Langlands Program with the ambitious goal of relating deep questions in Number Theory to Harmonic Analysis [L]. In particular, Langlands conjectured that Galois representations and motives can be described in terms of the more tangible data of automorphic representations. A striking application of this general principle is...
متن کاملGauge Theory and Wild Ramification
The gauge theory approach to the geometric Langlands program is extended to the case of wild ramification. The new ingredients that are required, relative to the tamely ramified case, are differential operators with irregular singularities, Stokes phenomena, isomonodromic deformation, and, from a physical point of view, new surface operators associated with higher order singularities.
متن کاملRamifications of the Geometric Langlands Program
Introduction 1 1. The unramified global Langlands correspondence 5 2. Classical local Langlands correspondence 9 3. Geometric local Langlands correspondence over C 12 4. Center and opers 18 5. Opers vs. local systems 23 6. Harish–Chandra categories 26 7. Local Langlands correspondence: unramified case 30 8. Local Langlands correspondence: tamely ramified case 41 9. Ramified global Langlands cor...
متن کاملRepresentation theory, geometric Langlands duality and categorification
The representation theory of reductive groups, such as the group GLn of invertible complex matrices, is an important topic, with applications to number theory, algebraic geometry, mathematical physics, and quantum topology. One way to study this representation theory is through the geometric Satake correspondence (also known as geometric Langlands duality). This correspondence relates the geome...
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ژورنال
عنوان ژورنال: Current Developments in Mathematics
سال: 2006
ISSN: 1089-6384,2164-4829
DOI: 10.4310/cdm.2006.v2006.n1.a2