Related papers: Equivariant mirror symmetry for footballs

In this paper, we establish equivariant mirror symmetry for the weighted projective line. This extends the results by B. Fang, C.C. Liu and Z. Zong, where the projective line was considered [{\it Geometry \& Topology} 24:2049-2092, 2017].…

We establish an unfolding theorem for equivariant F-bundles (a variant of Frobenius manifolds), generalizing Hertling-Manin's universal unfolding of meromorphic connections. As an application, we obtain the mirror symmetry theorem for the…

In this article, we establish homological Berglund--H\"ubsch mirror symmetry for curve singularities where the A--model incorporates equivariance, otherwise known as homological Berglund--H\"ubsch--Henningson mirror symmetry, including for…

We obtain A- and B- series of flag manifolds for T-equivariant tangent bundles and equivariant Chern polynomial following the arguments of Lian, Liu, Yau.

We study the equivariantly perturbed mirror Landau-Ginzburg model of the projective line. We show that the Eynard-Orantin recursion on this model encodes all genus all descendants equivariant Gromov-Witten invariants of the projective line.…

We found an explicit description of all $GL(n,\RR)$-Whittaker functions as oscillatory integrals and thus constructed equivariant mirrors of flag manifolds. As a consequence we proved the Virasoro conjecture for flag manifolds.

We construct functors sending torus-equivariant quasi-coherent sheaves on toric schemes over the sphere spectrum to constructible sheaves of spectra on real vector spaces. This provides a spectral lift of the toric homolgoical mirror…

Mirror symmetry relates Gromov-Witten invariants of an elliptic curve with certain integrals over Feynman graphs. We prove a tropical generalization of mirror symmetry for elliptic curves, i.e., a statement relating certain labeled…

In this paper we define an equivariant Floer $A_\infty$ algebra for $\mathbb{C}$ and $\mathbb{C} P^1$ by using Cartan model. We then prove an equivariant homological mirror symmetry, i.e. an equivalence between an $A_\infty$ category of…

Rietsch constructed a candidate $T$-equivariant mirror LG model for any flag variety $G/P$. In this paper, we prove the following mirror symmetry prediction: the small $T\times\mathbb{G}_m$-equivariant quantum cohomology of $G/P$ equipped…

We prove the Landau-Ginzburg mirror symmetry conjecture between invertible quasi-homogeneous polynomial singularities at all genera. That is, we show that the FJRW theory (LG A-model) of such a polynomial is equivalent to the Saito-Givental…

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…

In this paper we extend the discussion on Homological Mirror Symmetry for Fano toric varieties presented by Hori and Vafa to more general case of monotone symplectic manifolds with real polarizations. We claim that the Hori -- Vafa…

We develop general theory of equivariant quantum cohomology for ample Kahler manifolds and prove the mirror conjecture for projective complete intersections.

In this paper we complete the proof began by A. Polishchuk and E. Zaslow (math.AG/9801119) of a weak version of Kontsevich's homological mirror symmetry conjecture for elliptic curves. The main difference to the work of Polishchuk and…

We give details of models for rational torus equivariant homotopy theory based on (a) all subgroups, connected subgroups or dimensions of subgroups and (b) on pairs or general flags. We provide comparison functors and show the models are…

Landau-Ginzburg mirror symmetry studies isomorphisms between A- and B-models, which are graded Frobenius algebras that are constructed using a weighted homogeneous polynomial $W$ and a related group of symmetries $G$ of $W$. It is known…

In this short note we prove that in the case of elliptic curves, the isomorphism of generalized complex structure between $T$-dual manifolds described by Cavalcanti-Gualtieri coincides with the mirror map for elliptic curves described by…

We extend to orbifolds the quasimap theory of arXiv:0908.4446 and arXiv:1106.3724, as well as the genus zero wall-crossing results from arXiv:1304.7056 and arXiv:1401.7417. As a consequence, we obtain generalizations of orbifold mirror…

Building on work of Furstenberg and Tzkoni, we introduce ${\bf r}$-flag affine quermassintegrals and their dual versions. These quantities generalize affine and dual affine quermassintegrals as averages on flag manifolds (where the…