Sectorial descent for wrapped Fukaya categories
S Ganatra, J Pardon, V Shende - arXiv preprint arXiv:1809.03427, 2018 - arxiv.org
We develop a set of tools for doing computations in and of (partially) wrapped Fukaya
categories. In particular, we prove (1) a descent (cosheaf) property for the wrapped Fukaya …
categories. In particular, we prove (1) a descent (cosheaf) property for the wrapped Fukaya …
Mirror symmetry for very affine hypersurfaces
B Gammage, V Shende - Acta Mathematica, 2022 - projecteuclid.org
We show that the category of coherent sheaves on the toric boundary divisor of a smooth
quasi-projective toric DM stack is equivalent to the wrapped Fukaya category of a …
quasi-projective toric DM stack is equivalent to the wrapped Fukaya category of a …
Deformation quantization and perverse sheaves
S Gunningham, P Safronov - arXiv preprint arXiv:2312.07595, 2023 - arxiv.org
Kashiwara, Polesello, Schapira and D'Agnolo defined canonical deformation quantizations
of a holomorphic symplectic manifold and a holomorphic Lagrangian submanifold equipped …
of a holomorphic symplectic manifold and a holomorphic Lagrangian submanifold equipped …
Lagrangian skeleta and plane curve singularities
R Casals - Journal of Fixed Point Theory and Applications, 2022 - Springer
We construct closed arboreal Lagrangian skeleta associated to links of isolated plane curve
singularities. This yields closed Lagrangian skeleta for Weinstein pairs (C 2, Λ) and …
singularities. This yields closed Lagrangian skeleta for Weinstein pairs (C 2, Λ) and …
Wrapped sheaves
C Kuo - Advances in Mathematics, 2023 - Elsevier
We construct a sheaf-theoretic analogue of the wrapped Fukaya category in Lagrangian
Floer theory, by localizing a category of sheaves microsupported away from some given Λ⊂ …
Floer theory, by localizing a category of sheaves microsupported away from some given Λ⊂ …
On the Rouquier dimension of wrapped Fukaya categories and a conjecture of Orlov
S Bai, L Côté - Compositio Mathematica, 2023 - cambridge.org
We study the Rouquier dimension of wrapped Fukaya categories of Liouville manifolds and
pairs, and apply this invariant to various problems in algebraic and symplectic geometry. On …
pairs, and apply this invariant to various problems in algebraic and symplectic geometry. On …
Homological mirror symmetry at large volume
B Gammage, V Shende - Tunisian Journal of Mathematics, 2023 - msp.org
A typical large complex-structure limit for mirror symmetry consists of toric varieties glued to
each other along their toric boundaries. Here we construct the mirror large volume limit …
each other along their toric boundaries. Here we construct the mirror large volume limit …
Hypertoric Fukaya categories and categories O
L Côté, B Gammage, J Hilburn - arXiv preprint arXiv:2406.01379, 2024 - arxiv.org
To a conical symplectic resolution with Hamiltonian torus action, Braden--Proudfoot--Licata--
Webster associate a category O, defined using deformation quantization (DQ) modules. It …
Webster associate a category O, defined using deformation quantization (DQ) modules. It …
Mirror symmetry for Berglund-H\" ubsch Milnor fibers
B Gammage - arXiv preprint arXiv:2010.15570, 2020 - arxiv.org
We explain how to calculate the Fukaya category of the Milnor fiber of a Berglund-H\" ubsch
invertible polynomial, mostly proving a conjecture of Yank {\i} Lekili and Kazushi Ueda on …
invertible polynomial, mostly proving a conjecture of Yank {\i} Lekili and Kazushi Ueda on …
Non-abelian Hodge moduli spaces and homogeneous affine Springer fibers
R Bezrukavnikov, PB Alvarez, M McBreen… - arXiv preprint arXiv …, 2022 - arxiv.org
Starting from a homogeneous affine Springer fiber $ Fl_ {\psi} $, we construct three moduli
spaces that correspond to the Dolbeault, de Rham and Betti aspects of a hypothetical …
spaces that correspond to the Dolbeault, de Rham and Betti aspects of a hypothetical …