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math.SG2025
Skein-valued mirror curves for toric CY3 strips
Mingyuan Hu, Vivek Shende
For a smooth semi-projective toric Calabi-Yau 3-fold containing no compact surface, we show the count of all-genus holomorphic curves with boundary on a single Aganagic-Vafa brane…
math.SG2025
Microsheaf composition of Lagrangian correspondences
Wenyuan Li, David Nadler, Vivek Shende
In exact symplectic manifolds whose Liouville flow is gradientlike for a proper Morse function, one can associate conic microsheaves to eventually conic exact Lagrangians. Here we…
math.SG2024
Toric mirror monodromies and Lagrangian spheres
Vivek Shende
The central fiber of a Gross-Siebert type toric degeneration is known to satisfy homological mirror symmetry: its category of coherent sheaves is equivalent to the wrapped Fukaya c…