In mathematics, the geometric Langlands correspondence is a reformulation of the Langlands correspondence obtained by replacing the number fields appearing in the original number theoretic version by function fields and applying techniques from algebraic geometry.[1] The geometric Langlands correspondence relates algebraic geometry and representation theory.
The specific case of the geometric Langlands correspondence for general linear groups over function fields was proven by Laurent Lafforgue in 2002, where it follows as a consequence of Lafforgue's theorem.
^Cite error: The named reference Frenkel 2007, p. 3 was invoked but never defined (see the help page).
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geometricLanglandscorrespondence relates algebraic geometry and representation theory. The specific case of the geometricLanglandscorrespondence for...
research, the Langlands program has been described by Edward Frenkel as "a kind of grand unified theory of mathematics." The Langlands program consists...
through the notions of elliptic module and the theory of the geometricLanglandscorrespondence. Drinfeld introduced the notion of a quantum group (independently...
Phelan Langlands, CC FRS FRSC (/ˈlæŋləndz/; born October 6, 1936) is a Canadian mathematician. He is best known as the founder of the Langlands program...
and Kari Vilonen, he has proved the geometricLanglands conjecture for GL(n). His joint work with Robert Langlands and Ngô Bảo Châu suggested a new approach...
geometry, a branch of mathematics that describes geometric shapes in algebraic terms and solves geometric problems using algebraic equations. On the other...
ISBN 978-0-691-18443-2. On the geometricLanglands conjecture On a vanishing conjecture appearing in the geometricLanglandscorrespondence Dennis Gaitsgory at the...
Anton; Witten, Edward (2007). "Electric-magnetic duality and the geometricLanglands program". Communications in Number Theory and Physics. 1 (1): 1–236...
mathematical contexts such as monstrous moonshine and the geometricLanglandscorrespondence. The related notion of vertex algebra was introduced by Richard...
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integrable system theory. It also plays an important role in the geometricLanglandscorrespondence over the field of complex numbers through conformal field...
mathematical connections between S-duality of gauge theories and the geometricLanglandscorrespondence. Partly in collaboration with Seiberg, one of his recent interests...
Chern–Simons theory, Gromov–Witten invariants, mirror symmetry, geometricLanglands Program, and many other topics. The operators in topological string...
Yang–Mills theory, a gauge theory. This conjecture, called the AdS/CFT correspondence, has generated a great deal of interest in high energy physics. It is...
between the S-duality of supersymmetric gauge theories and the geometricLanglandscorrespondence. In recent years, he has focused on mathematical structures...
't Hooft limit; it was the first suggestion concerning the AdS/CFT correspondence. In the late 1980s, it was realized that type IIA string theory is related...
)}g(\xi )} Since the world-sheet is two dimensional, there is a 1-1 correspondence between conformal structures and complex structures. One still has to...
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