137 citations · 377 across the 17 of their papers we have counts for
18 papers
The cyclic open--closed map and variations of Hodge structures
Sheel Ganatra, Nick Sheridan
We construct the cyclic open--closed map for the big (i.e., bulk-deformed) relative Fukaya category, in the semipositive case, and show that it is a morphism of `polarized variatio…
King's Conjecture and the Cox category
Matthew R. Ballard, Christine Berkesch, Michael K. Brown +6
We state and prove a realization of King's Conjecture for a category glued from the derived categories of all of the toric varieties arising from a given Cox ring. Our perspective…
Homological mirror symmetry for Batyrev mirror pairs
Sheel Ganatra, Andrew Hanlon, Jeff Hicks +2
We prove Kontsevich's homological mirror symmetry conjecture for a large class of mirror pairs of Calabi--Yau hypersurfaces in toric varieties. These mirror pairs were constructed…
Integrality of mirror maps and arithmetic homological mirror symmetry for Greene--Plesser mirrors
Sheel Ganatra, Andrew Hanlon, Jeff Hicks +2
We prove the `integrality of Taylor coefficients of mirror maps' conjecture for Greene--Plesser mirror pairs as a natural byproduct of an arithmetic refinement of homological mirro…
Rabinowitz Fukaya categories and the categorical formal punctured neighborhood of infinity
Sheel Ganatra, Yuan Gao, Sara Venkatesh
This paper constructs and studies the Rabinowitz (wrapped) Fukaya category, a categorical invariant of exact cylindrical Lagrangians in a Liouville manifold whose cohomological mor…
Categorical non-properness in wrapped Floer theory
Sheel Ganatra
In all known explicit computations on Weinstein manifolds, the self-wrapped Floer homology of non-compact exact Lagrangian is always either infinite-dimensional or zero. We show th…
On the embedding complexity of Liouville manifolds
Sheel Ganatra, Kyler Siegel
We define a family of symplectic invariants which obstruct exact symplectic embeddings between Liouville manifolds, using the general formalism of linearized contact homology and i…
Cyclic homology, -equivariant Floer cohomology, and Calabi-Yau structures
Sheel Ganatra
We construct geometric maps from the cyclic homology groups of the (compact or wrapped) Fukaya category to the corresponding -equivariant (Floer/quantum or symplectic) cohomol…
Symplectic cohomology rings of affine varieties in the topological limit
Sheel Ganatra, Daniel Pomerleano
We construct a multiplicative spectral sequence converging to the symplectic cohomology ring of any affine variety , with first page built out of topological invariants associat…
Microlocal Morse theory of wrapped Fukaya categories
Sheel Ganatra, John Pardon, Vivek Shende
The Nadler--Zaslow correspondence famously identifies the finite-dimensional Floer homology groups between Lagrangians in cotangent bundles with the finite-dimensional Hom spaces b…
Sectorial descent for wrapped Fukaya categories
Sheel Ganatra, John Pardon, Vivek Shende
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 ca…
The Gamma and Strominger-Yau-Zaslow conjectures: a tropical approach to periods
Mohammed Abouzaid, Sheel Ganatra, Hiroshi Iritani +1
We propose a new method to compute asymptotics of periods using tropical geometry, in which the Riemann zeta values appear naturally as error terms in tropicalization. Our method s…
Covariantly functorial wrapped Floer theory on Liouville sectors
Sheel Ganatra, John Pardon, Vivek Shende
We introduce a class of Liouville manifolds with boundary which we call Liouville sectors. We define the wrapped Fukaya category, symplectic cohomology, and the open-closed map for…
A Log PSS morphism with applications to Lagrangian embeddings
Sheel Ganatra, Daniel Pomerleano
Let be a smooth projective variety and an ample normal crossings divisor. From topological data associated to the pair , we construct, under assum…
Automatically generating Fukaya categories and computing quantum cohomology
Sheel Ganatra
Suppose one has found a non-empty sub-category of the Fukaya category of a compact Calabi-Yau manifold which is homologically smooth in the sense of non-commutati…
Mirror symmetry: from categories to curve counts
Sheel Ganatra, Timothy Perutz, Nick Sheridan
We work in the setting of Calabi-Yau mirror symmetry. We establish conditions under which Kontsevich's homological mirror symmetry (which relates the derived Fukaya category to the…
Flexible Lagrangians
Yakov Eliashberg, Sheel Ganatra, Oleg Lazarev
We introduce and discuss notions of regularity and flexibility for Lagrangian manifolds with Legendrian boundary in Weinstein domains. There is a surprising abundance of flexible L…
Symplectic cohomology and duality for the wrapped Fukaya category
Sheel Ganatra
Consider the wrapped Fukaya category W of a collection of exact Lagrangians in a Liouville manifold. Under a non-degeneracy condition implying the existence of enough Lagrangians,…