The computation of scattering amplitudes in gauge theories is given an impetus by

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The computation of scattering amplitudes in gauge theories is given an   impetus by

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the cross-fertilization between mathematics and physics

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the practical problem of computing backgrounds for the Large Hadron Collider

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the reformulation of the geometric Langlands program in terms of quantum field theory

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using  the tools of algebraic geometry and some methods from geometric number theory

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