115 citations · 241 across the 11 of their papers we have counts for
16 papers
Rigidity, flexibility, and a sign error
Yanki Lekili, Nick Sheridan
The documents [OAI26a, OAI26b, OAI26c] claimed to prove cases of the Hodge conjecture via homological mirror symmetry, before being withdrawn by OpenAI. We discuss the source of th…
Constructing the relative Fukaya category
Timothy Perutz, Nick Sheridan
We give a definition of Seidel's `relative Fukaya category', for a smooth complex projective variety, under a semipositivity assumption. We use the Cieliebak--Mohnke approach to tr…
Quantum cohomology as a deformation of symplectic cohomology
Matthew Strom Borman, Nick Sheridan, Umut Varolgunes
We prove that under certain conditions, the quantum cohomology of a positively monotone compact symplectic manifold is a deformation of the symplectic cohomology of the complement…
Rational equivalence and Lagrangian tori on K3 surfaces
Nick Sheridan, Ivan Smith
Fix a symplectic K3 surface X homologically mirror to an algebraic K3 surface Y by an equivalence taking a graded Lagrangian torus L in X to the skyscraper sheaf of a point y of Y.…
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…
Lagrangian cobordism and tropical curves
Nick Sheridan, Ivan Smith
We study a cylindrical Lagrangian cobordism group for Lagrangian torus fibres in symplectic manifolds which are the total spaces of smooth Lagrangian torus fibrations. We use ideas…
Versality in mirror symmetry
Nick Sheridan
One of the attractions of homological mirror symmetry is that it not only implies the previous predictions of mirror symmetry (e.g., curve counts on the quintic), but it should in…
Symplectic topology of K3 surfaces via mirror symmetry
Nick Sheridan, Ivan Smith
We study the symplectic topology of certain K3 surfaces (including the "mirror quartic" and "mirror double plane"), equipped with certain Kähler forms. In particular, we prove that…
Homological mirror symmetry for generalized Greene-Plesser mirrors
Nick Sheridan, Ivan Smith
We prove Kontsevich's homological mirror symmetry conjecture for certain mirror pairs arising from Batyrev-Borisov's `dual reflexive Gorenstein cones' construction. In particular w…
Versality of the relative Fukaya category
Nick Sheridan
Seidel introduced the notion of a Fukaya category `relative to an ample divisor', explained that it is a deformation of the Fukaya category of the affine variety that is the comple…
Automatic split-generation for the Fukaya category
Timothy Perutz, Nick Sheridan
We prove a structural result in mirror symmetry for projective Calabi--Yau (CY) manifolds. Let be a connected symplectic CY manifold, whose Fukaya category is…
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…
Formulae in noncommutative Hodge theory
Nick Sheridan
We prove that the cyclic homology of a saturated category admits the structure of a `polarized variation of Hodge structures', building heavily on the work of many autho…
On the Fukaya category of a Fano hypersurface in projective space
Nick Sheridan
This paper is about the Fukaya category of a Fano hypersurface . Because these symplectic manifolds are monotone, both the analysis and the algebra involve…
Homological Mirror Symmetry for Calabi-Yau hypersurfaces in projective space
Nicholas Sheridan
We prove Homological Mirror Symmetry for a smooth d-dimensional Calabi-Yau hypersurface in projective space, for any d > 2 (for example, d = 3 is the quintic three-fold). The main…
On the homological mirror symmetry conjecture for pairs of pants
Nicholas Sheridan
The n-dimensional pair of pants is defined to be the complement of n+2 generic hyperplanes in CP^n. We construct an immersed Lagrangian sphere in the pair of pants and compute its…