Related papers: Noncommutative homological mirror symmetry of elli…
The derived category of coherent sheaves $\mathcal{T}_B$ associated to a birational cobordism which is either a weighted projective space, a stacky Atiyah flip, or a stacky blow-up of a point has a conjectural mirror Fukaya-Seidel category…
We give a survey on results related to the Berglund-H\"ubsch duality of invertible polynomials and the homological mirror symmetry conjecture for singularities.
We carry out the SYZ program for the local Calabi--Yau manifolds of type $\widetilde{A}$ by developing an equivariant SYZ theory for the toric Calabi--Yau manifolds of infinite-type. Mirror geometry is shown to be expressed in terms of the…
We study topological strings on non-commutative resolutions of singular Calabi-Yau threefolds that are double covers of $\mathbb{P}^3$, ramified over determinantal octic surfaces. Using conifold transitions to complete intersections in…
We compute Przyjalkowski-Shramov's resolution of the Calabi-Yau compactification of Givental's mirror Landau-Ginzburg model of the quadric hypersurfaces. We deduce the Picard-Fuchs equation for the narrow periods, which mirror the ambient…
We consider an (N-2)-dimensional Calabi-Yau manifold which is defined as the zero locus of the polynomial of degree N (of Fermat type) in CP^{N-1} and its mirror manifold. We introduce the (N-2)-point correlation function (generalized…
We construct a wide class of non-geometric compactifications of type II superstring theories preserving N=1 space-time supersymmetry in four dimensions, starting from Calabi-Yau compactifications at Gepner points. Particular examples of…
We construct A-infinity functors between Fukaya categories associated to monotone Lagrangian correspondences between compact symplectic manifolds. We then show that the composition of A-infinity functors for correspondences is homotopic to…
We propose and prove a mirror theorem for the elliptic quasimap invariants for smooth Calabi-Yau complete intersections in projective spaces. The theorem combined with the wall-crossing formula appeared in paper (arXiv:1308.6377) implies…
We study Landau Ginzburg (LG) theories mirror to 2D N=2 gauged linear sigma models on toric Calabi-Yau manifolds. We derive and solve new constraint equations for Landau Ginzburg elliptic Calabi-Yau superpotentials, depending on the…
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 variations of semi-infinite Hodge structures'. We also give a…
The asymptotic behaviour of solutions to the quantum differential equation of a Fano manifold F defines a characteristic class A_F of F, called the principal asymptotic class. Gamma conjecture of Vasily Golyshev and the present authors…
The present paper is aimed to discussing three kinds of problems: (1) producing some ``mirror theorem'' for the recent mirror symmetric construction, called \emph{framed} duality ($f$-duality), described in \cite{R-fTV} and \cite{R-fpCI}:…
We give an example of the recent proposed mirror construction of Strominger, Yau and Zaslow in ``Mirror Symmetry is T-duality,'' hep-th/9606040. The paper first considers mirror symmetry for K3 surfaces in light of this construction. We…
The nonequivariant coherent-costructible correspondence is a microlocal-geometric interpretation of homological mirror symmetry for toric varieties conjectured by Fang-Liu-Treumann-Zaslow. We prove a generalization of this conjecture for a…
We present an algorithm for determining all inequivalent abelian symmetries of non-degenerate quasi-homogeneous polynomials and apply it to the recently constructed complete set of Landau--Ginzburg potentials for $N=2$ superconformal field…
We prove the homological mirror symmetry conjecture of Kontsevich for K3 surfaces in the following form: The Fukaya category of a projective K3 surface is equivalent to the derived category of coherent sheaves on the mirror, which is a K3…
We construct a class of exactly solved (0,2) heterotic compactifications, similar to the (2,2) models constructed by Gepner. We identify these as special points in moduli spaces containing geometric limits described by non-linear sigma…
This paper discusses homological mirror symmetry for the Fargues-Fontaine curve of equal characteristic.
Given a smooth projective variety $X$ with a smooth anticanonical divisor $D$, we study mirror symmetry for the log Calabi--Yau pair $(X,D)$ without assuming that $D$ is nef. We consider the mirror proper Landau--Ginzburg model $(\check…