Localization and mirror symmetry

Mirror Symmetry and Localization

Equivariant Localization and Mirror Symmetry

Log Mirror Symmetry and Local Mirror Symmetry

We study Mirror Symmetry of log Calabi-Yau surfaces. On one hand, we consider the number of “affine lines” of each degree in P\B, where B is a smooth cubic. On the other hand, we consider coefficients of a certain expansion of a function obtained from the integrals of dx/x ∧ dy/y over 2chains whose boundaries lie on Bφ, where {Bφ} is a family of smooth cubics. Then, for small degrees, they coin...

Mirror Symmetry and Localizations

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 the computations on complicated moduli spaces to simple moduli spaces. It is a key technique in the proof of the general mirror formula, the proof of the Hori-Vafa formula for explicit expressions...

Mirror Symmetry and C

We show that counting functions of covers of C× are equal to sums of integrals associated to certain ‘Feynman’ graphs. This is an analogue of the mirror symmetry for elliptic curves.