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Award ID contains: 2416129

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  1. ; (, Annals of Mathematics)
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  2. ; (, Journal of the American Mathematical Society)
    We calculate the category of D D -modules on the loop space of the affine line in coherent terms. Specifically, we find that this category is derived equivalent to the category of ind-coherent sheaves on the moduli space of rank one de Rham local systems with a flat section. Our result establishes a conjecture coming out of the 3 d 3d mirror symmetry program, which obtains new compatibilities for the geometric Langlands program from rich dualities of QFTs that are themselves obtained from string theory conjectures. 
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  3. ; (, Bulletin of the London Mathematical Society)
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  4. ; (, Bulletin of the London Mathematical Society)
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  5. (, Annals of Mathematics)
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  6. ; ; (, Compositio Mathematica)
    In quantum geometric Langlands, the Satake equivalence plays a less prominent role than in the classical theory. Gaitsgory and Lurie proposed a conjectural substitute, later termed the fundamental local equivalence . With a few exceptions, we prove this conjecture and its extension to the affine flag variety by using what amount to Soergel module techniques. 
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  7. (, Compositio Mathematica)
    We establish some cohomological bounds in $$D$$ -module theory that are known in the holonomic case and folklore in general. The method rests on a generalization of the $$b$$ -function lemma for non-holonomic $$D$$ -modules. 
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