More on gauge theory and geometric Langlands
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 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...
متن کاملOn the Geometric Langlands Conjecture
0.1. Background. Let X be a smooth, complete, geometrically connected curve over the finite field Fq. Denote by F the field of rational functions on X and by A the ring of adèles of F . The Langlands conjecture, recently proved by L. Lafforgue [Laf], establishes a correspondence between cuspidal automorphic forms on the group GLn(A) and irreducible, almost everywhere unramified, n–dimensional `...
متن کاملA Note on Quantum Geometric Langlands Duality, Gauge Theory, and Quantization of the Moduli Space of Flat Connections
Montonen-Olive duality implies that the categories of A-branes on the moduli spaces of Higgs bundles on a Riemann surface C for groups G and G are equivalent. We reformulate this as a statement about categories of B-branes on the quantized moduli spaces of flat connections for groups GC and GC. We show that it implies the statement of the Quantum Geometric Langlands duality with a purely imagin...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2018
ISSN: 0001-8708
DOI: 10.1016/j.aim.2017.06.021