Related papers: Mirror symmetry for abelian varieties
We prove the Mirror Conjecture for Calabi-Yau manifolds equipped with a holomorphic symplectic form. Such manifolda are also known as complex manifolds of hyperkaehler type. We obtain that a complex manifold of hyperkaehler type is Mirror…
We continue classification of finite groups which can be used as symmetry group of the scalar sector of the four-Higgs-doublet model (4HDM). Our objective is to systematically construct non-abelian groups via the group extension procedure,…
Symmetric homology is an analog of cyclic homology in which the cyclic groups are replaced by symmetric groups. The foundations for the theory of symmetric homology of algebras are developed in the context of crossed simplicial groups using…
This work provides a comprehensive theoretical framework for understanding the symmetry properties of High-Resolution NMR spectra. We analyze the conditions under which a spectrum exhibits mirror symmetry (palindromicity). We demonstrate…
We explicitly apply localization results to study the interpolation between three and two dimensional mirror symmetry for Abelian gauge theories with four supercharges. We first use the ellipsoid S_b^3 partition functions to verify the…
We study aspects related to Kontsevich's homological mirror symmetry conjecture in the case of Calabi-Yau complete intersections in toric varieties. In a 1996 lecture at Rutgers University, Kontsevich indicated how his proposal implies that…
We study homological mirror symmetry for not necessarily compactly supported coherent sheaves on the minimal resolutions of A_n-singularities. An emphasis is put on the relation with the Strominger-Yau-Zaslow conjecture.
We solved the long-standing problem of describing the cohomology ring of semiample hypersurfaces in complete simplicial toric varieties. Also, the monomial-divisor mirror map is generalized to a map between the whole Picard group and the…
We revisit our construction of mirror symmetries for compactifications of Type II superstrings on twisted connected sum $G_2$ manifolds. For a given $G_2$ manifold, we discuss evidence for the existence of mirror symmetries of two kinds:…
We prove Kontsevich's homological mirror symmetry conjecture for certain mirror pairs arising from Batyrev-Borisov's `dual reflexive Gorenstein cones' construction. In particular we prove HMS for all Greene-Plesser mirror pairs (i.e.,…
The existence of a new kind of branes for the open topological A-model is argued by using the generalized complex geometry of Hitchin and the SYZ picture of mirror symmetry. Mirror symmetry suggests to consider a bi-vector in the normal…
We prove homological mirror symmetry for the universal centralizer $J_G$ (a.k.a the Toda space), associated to any complex reductive Lie group $G$. The A-side is a partially wrapped Fukaya category on $J_G$, and the B-side is the category…
Garoufalidis and Levine introduced the homology cobordism group of homology cylinders over a surface. This group can be regarded as a generalization of the mapping class group. Using torsion invariants, we show that the abelianization of…
The goal of this paper is to propose a theory of mirror symmetry for varieties of general type. Using Landau-Ginzburg mirrors as motivation, we describe the mirror of a hypersurface of general type (and more generally varieties of…
In this article, we revisit the classical McKay correspondence via homological mirror symmetry. Specifically, we demonstrate how this correspondence can be articulated as a derived equivalence between the category of vanishing cycles…
Given a smooth toric variety X and an ample line bundle O(1), we construct a sequence of Lagrangian submanifolds of (C^*)^n with boundary on a level set of the Landau-Ginzburg mirror of X. The corresponding Floer homology groups form a…
We study the representation of a finite group acting on the cohomology of a non-degenerate, invariant hypersurface of a projective toric variety. We deduce an explicit description of the representation when the toric variety has at worst…
I provide two solutions to the problem of categorifying quantum link invariants, which work uniformly for all gauge groups and originate in geometry and string theory. The first is based on a category of equivariant B-type branes on ${\cal…
This is a survey of results and conjectures on mirror symmetry phenomena in the non-Abelian Hodge theory of a curve. We start with the conjecture of Hausel-Thaddeus which claims that certain Hodge numbers of moduli spaces of flat SL(n,C)…
Mirror symmetry relates type IIB string theory on a Calabi-Yau 3-fold to type IIA on the mirror CY manifold, whose complex structure and Kaehler moduli spaces are exchanged. We show that the mirror map is a particular case of a more general…