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The Langlands program and . . .
, 2006
"... A number theoretic approach to string compactification is developed for CalabiYau hypersurfaces in arbitrary dimensions. The motivic strategy involved is illustrated by showing that the Hecke eigenforms derived from Galois group orbits of the holomorphic twoform of a particular type of K3 surfaces ..."
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A number theoretic approach to string compactification is developed for CalabiYau hypersurfaces in arbitrary dimensions. The motivic strategy involved is illustrated by showing that the Hecke eigenforms derived from Galois group orbits of the holomorphic twoform of a particular type of K3 surfaces can be expressed in terms of modular forms constructed from the worldsheet theory. The process of deriving string physics from spacetime geometry can be reversed, allowing the construction of K3 surface geometry from the string characters of the partition function. A general argument for K3 modularity follows from mirror symmetry, in combination with the proof of the ShimuraTaniyama conjecture.
ElectricMagnetic duality and the geometric Langlands program
, 2006
"... The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N = 4 super YangMills theory in four dimensions. The key ingredients are electricmagnetic duality of gauge theory, mirror symmetry of sigmamodels, branes, Wilson and ’t H ..."
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Cited by 300 (26 self)
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The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N = 4 super YangMills theory in four dimensions. The key ingredients are electricmagnetic duality of gauge theory, mirror symmetry of sigmamodels, branes, Wilson and ’t
THE LANGLANDS PROGRAM: NOTES, DAY I
, 2014
"... Abstract. These are notes for the first of a twoday series of lectures introducing graduate students to (parts of) the Langlands Program, delivered in the Building ..."
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Abstract. These are notes for the first of a twoday series of lectures introducing graduate students to (parts of) the Langlands Program, delivered in the Building
Recent advances in the Langlands program
 Bull. Amer. Math. Soc
"... Abstract. These are the notes for the lecture given by the author at the “Mathematical Current Events ” Special Session of the AMS meeting in Baltimore on January 17, 2003. Topics reviewed include the Langlands correspondence for GL(n) in the function field case and its proof by V. Drinfeld and L. L ..."
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Cited by 16 (3 self)
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Abstract. These are the notes for the lecture given by the author at the “Mathematical Current Events ” Special Session of the AMS meeting in Baltimore on January 17, 2003. Topics reviewed include the Langlands correspondence for GL(n) in the function field case and its proof by V. Drinfeld and L
Introduction to the Langlands Program
"... This article is an introduction to automorphic forms on the adeles of a linear reductive group over a number field. The first half is a summary of aspects of local and global class field theory, with emphasis on the local Weil group, the L functions ..."
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This article is an introduction to automorphic forms on the adeles of a linear reductive group over a number field. The first half is a summary of aspects of local and global class field theory, with emphasis on the local Weil group, the L functions
LANGLANDS PROGRAM, TRACE FORMULAS, AND THEIR GEOMETRIZATION
, 2012
"... Abstract. The Langlands Program relates Galois representations and automorphic representations of reductive algebraic groups. The trace formula is a powerful tool in the study of this connection and the Langlands Functoriality Conjecture. After giving an introduction to the Langlands Program and its ..."
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Cited by 2 (0 self)
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Abstract. The Langlands Program relates Galois representations and automorphic representations of reductive algebraic groups. The trace formula is a powerful tool in the study of this connection and the Langlands Functoriality Conjecture. After giving an introduction to the Langlands Program
Lectures on ElectricMagnetic Duality and the Geometric Langlands Program
, 2008
"... These lecture notes are based on the master class given at the Center for the Topology and Quantization of Moduli Spaces, University of Aarhus, August 2007. I provide an introduction to the recent work on the MontonenOlive duality of N = 4 superYangMills theory and the Geometric Langlands Progra ..."
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These lecture notes are based on the master class given at the Center for the Topology and Quantization of Moduli Spaces, University of Aarhus, August 2007. I provide an introduction to the recent work on the MontonenOlive duality of N = 4 superYangMills theory and the Geometric Langlands
Gauging Spacetime Symmetries On The Worldsheet And The Geometric Langlands Program
, 710
"... We study the twodimensional twisted (0, 2) sigmamodel on various smooth complex flag manifolds G/B, and explore its relevance to the geometric Langlands program. We find that an equivalence at the level of the holomorphic chiral algebra between a bosonic string on G/B and a Bgauged version of i ..."
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Cited by 2 (0 self)
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We study the twodimensional twisted (0, 2) sigmamodel on various smooth complex flag manifolds G/B, and explore its relevance to the geometric Langlands program. We find that an equivalence at the level of the holomorphic chiral algebra between a bosonic string on G/B and a Bgauged version
QuasiTopological Gauged Sigma Models, The Geometric Langlands Program, And Knots
"... We construct and study a closed, twodimensional, quasitopological (0, 2) gauged sigma model with target space a smooth Gmanifold, where G is any compact and connected Lie group. When the target space is a flag manifold of simple G, and the gauge group is a Cartan subgroup thereof, the perturbativ ..."
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, the perturbative model describes, purely physically, the recently formulated mathematical theory of “Twisted Chiral Differential Operators”. This paves the way, via a generalized Tduality, for a natural physical interpretation of the geometric Langlands correspondence for simplyconnected, simple, complex Lie
Results 1  10
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2,243