A geometric realization of the principal block of quantum group modules at roots of unity is established as microsheaves on an affine Springer fiber, together with a wild-ramification geometric Langlands equivalence to coherent sheaves on the dual Springer resolution.
Sheaf quantization in
4 Pith papers cite this work. Polarity classification is still indexing.
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2026 4verdicts
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Proves that the wrapped microlocal sheaf category μSh^w_L(L) is equivalent to Coh(X^∘) for conic bundle mirrors of toric Calabi-Yau (n+2)-folds under given conditions.
Proves homological mirror symmetry equivalence between Fukaya categories of generic-microlocal-monodromy moduli and coherent sheaves on minimal resolutions of trivial-microlocal-monodromy moduli for rank-two local systems on the projective line.
Three topological invariants classify generating functions for Legendrians up to stabilization and fiberwise diffeomorphism.
citing papers explorer
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Affine Springer fiber and the small quantum group
A geometric realization of the principal block of quantum group modules at roots of unity is established as microsheaves on an affine Springer fiber, together with a wild-ramification geometric Langlands equivalence to coherent sheaves on the dual Springer resolution.
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Homological Mirror Symmetry for Conic Bundle
Proves that the wrapped microlocal sheaf category μSh^w_L(L) is equivalent to Coh(X^∘) for conic bundle mirrors of toric Calabi-Yau (n+2)-folds under given conditions.
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Mirror symmetry for the Painlev\'e character varieties
Proves homological mirror symmetry equivalence between Fukaya categories of generic-microlocal-monodromy moduli and coherent sheaves on minimal resolutions of trivial-microlocal-monodromy moduli for rank-two local systems on the projective line.
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A topological classification of generating functions
Three topological invariants classify generating functions for Legendrians up to stabilization and fiberwise diffeomorphism.