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Curvelets and Wave Atoms for Mirror-Extended Images
Curvelets Wave Atoms Mirror-Extended Images
2015/7/15
We present variants of both the digital curvelet transform, and the digital wave atom transform, which handle the image boundaries by mirror extension. Previous versions of these transforms treated im...
A Note on Gluing Dirac Type Operators on a Mirror Quantum Two-Sphere
Gluing Dirac Type Operators Mirror Quantum Two-Sphere
2014/12/12
The goal of this paper is to introduce a class of operators, which we call quantum Dirac type operators on a noncommutative sphere, by a gluing construction from copies of noncommutative disks, subjec...
Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces
Lagrangian fibrations blowups of toric varieties mirror symmetry hypersurfaces Algebraic Geometry
2012/5/9
We consider mirror symmetry for (essentially arbitrary) hypersurfaces in (possibly noncompact) toric varieties from the perspective of the Strominger-Yau-Zaslow (SYZ) conjecture. Given a hypersurface ...
On the homological mirror symmetry conjecture for pairs of pants
homological mirror symmetry pairs of pants
2011/2/21
The n-dimensional pair of pants is defined to be the complement of n + 2 generic hyperplanes in CPn. We construct an immersed Lagrangian sphere in the pair of pants and compute its endomorphism A∞ alg...
We prove a representation-theoretic version of Borisov-Batyrev mirror symmetry, and use it to construct infinitely many new pairs of orbifolds with mirror Hodge diamonds, with respect to the usual Ho...
Lagrangian Floer theory and mirror symmetry on compact toric manifolds
Floer cohomology mirror symmetry toric manifolds open-closed Gromov-Witten invariant
2010/12/1
this paper we study Lagrangian Floer theory on toric manifolds from the point of view of mirror symmetry. We construct a natural isomorphism between the Frobenius manifold structures of the (big) quan...
Affine Manifolds, Log Structures, and Mirror Symmetry
Affine Manifolds Log Structures Mirror Symmetry
2010/3/1
We outline work in progress suggesting an algebro-geometric version of the Strominger-Yau-Zaslow conjecture. We define the notion of a toric degeneration, a special case of a maximally unipotent degen...
In this paper, using mirror principle developped by Lian, Liu and Yau [8, 9, 10, 11, 12, 13] we obtained the A and B series for the equivariant tangent bundles over homogenous spaces using Chern polyn...
We describe the applications of localization methods, in particular the functorial localization formula, in the proofs of several conjectures from string theory. Functorial localization formula pushes...
fixed-points in hyper-Quot-schemes and an exact mirror formula for flag manifolds from the extended mirror principle diagram
mirror principle flag manifold hyper-Quot-scheme S1-fixed-point hypergeometric series restrictive flag manifold tangent stack Euler sequence mirror symmetry Hori-Vafa formula Young tableau combinatorics
2018/4/20
In the series of work [L-L-Y1, III: Sec. 5.4] on mirror principle, two of the current authors (K.L. and S.-T.Y.) with Bong H. Lian developed a method to compute the integralR X τeH·t ∩ 1d for a flag ...
Mirror symmetry and actions of braid groups on derived categories
Mirror symmetry actions braid groups derived categories
2010/10/29
Talk given at Harvard, January 1999, published in the Proceedings of the Harvard Winter School on mirror symmetry, vector bundles and lagrangian cycles, 1999, International Press. Surveys the joint wo...