Related papers: Orbifold Quasimap Theory
We introduce a moduli space of ``complete quasimaps'' to $\mathsf{Bl}_{\mathbb{P}^s}(\mathbb{P}^r)$. The construction, following previous work for curves on projective spaces, essentially proceeds by blowing up Ciocan-Fontanine--Kim's space…
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 mirror symmetry. We also prove homological mirror symmetry for…
It is argued that every Calabi-Yau manifold $X$ with a mirror $Y$ admits a family of supersymmetric toroidal 3-cycles. Moreover the moduli space of such cycles together with their flat connections is precisely the space $Y$. The mirror…
We establish an upper estimate for the coefficient of quasiconformal reflection with respect to the boundary of an arbitrary isosceles trapezoid in terms of its geometric parameters; the estimate improve the result obtained in the recent…
A quasihomomorphism is a map that satisfies the homomorphism relation up to bounded error. Fujiwara and Kapovich proved a rigidity result for quasihomomorphisms taking values in discrete groups, showing that all quasihomomorphisms can be…
The mathematical physicists Bershadsky-Cecotti-Ooguri-Vafa (BCOV) proposed, in a seminal article from '94, a conjecture extending genus zero mirror symmetry to higher genera. With a view towards a refined formulation of the…
We construct a family of points on the Lagrangian cone of a partial flag bundle associated to a (possibly non-split) vector bundle from any Weyl-invariant $I$-function of a prequotient. This result can be seen as the nonabelian analogue of…
In this note, we give a short proof of the Torelli theorem for cubic fourfolds that relies on the global Torelli theorem for irreducible holomorphic symplectic varieties proved by Verbitsky.
The moduli spaces of stable quasimaps unify various moduli appearing in the study of Gromov-Witten Theory. This note is a survey article on the moduli of stable quasimaps, based on joint papers with Ciocan-Fontanine and Maulik as well as…
We study mirror symmetry for orbifold Hurwitz numbers. We show that the Laplace transform of orbifold Hurwitz numbers satisfy a differential recursion, which is then proved to be equivalent to the integral recursion of Eynard and Orantin…
Multiply-connected Calabi-Yau threefolds are of particular interest for both string theorists and mathematicians. Recently it was pointed out that one of the generic degenerations of these spaces (occurring at codimension one in moduli…
We prove the No Invariant Line Fields conjecture for a class of generalized postcritically-finite branched covers on higher-dimensional Riemannian manifolds. Moreover, we establish a quasisymmetric uniformization theorem for this class of…
We generalize the classical approach of describing the infinitesimal Torelli map in terms of multiplication in a Jacobi ring to the case of quasi-smooth complete intersections in weighted projective space. As an application, we prove the…
The connection between the theory of permutation orbifolds, covering surfaces and uniformization is investigated, and the higher genus partition functions of an arbitrary permutation orbifold are expressed in terms of those of the original…
We prove the equivariant Gromov-Witten theory of a nonsingular toric 3-fold X with primary insertions is equivalent to the equivariant Donaldson-Thomas theory of X. As a corollary, the topological vertex calculations by Agangic, Klemm,…
This article is a survey of a series of papers [FOOO3,FOOO4,FOOO5] in which we developed the method of calculation of Floer cohomology of Lagrangian torus orbits in compact toric manifolds, and its applications to symplectic topology and to…
We develop a mathematical framework for the computation of open orbifold Gromov-Witten invariants of [C^3/Z_n], and provide extensive checks with predictions from open string mirror symmetry. To this aim we set up a computation of open…
We show that certain isomorphisms of (twisted) KR-groups that underlie T-dualities of torus orientifold string theories have purely algebraic analogues in terms of algebraic K-theory of real varieties and equivalences of derived categories…
We give a mathematical account of a recent string theory calculation which predicts the number of rational curves on the generic quintic threefold. Our account involves the interpretation of Yukawa couplings in terms of variations of Hodge…
We prove the existence of invariant almost complex structure on any positively omnioriented quasitoric orbifold. We construct blowdowns. We define Chen-Ruan cohomology ring for any omnioriented quasitoric orbifold. We prove that the Euler…