Arithmetic 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 Localization

Meet Homological Mirror Symmetry

In this paper, we introduce the interested reader to homological mirror symmetry. After recalling a little background knowledge, we tackle the simplest cases of homological mirror symmetry: curves of genus zero and one. We close by outlining the current state of the field and mentioning what homological mirror symmetry has to say about other aspects of mirror symmetry.

Mirror symmetry in Dutch

Dutch PPs show mirror symmetry with respect to the embedded verb. In older theories, this was partially accounted for by an extraposition rule known as PP-over-V. In the theoretical framework adopted here, such rightward movements are no longer available. The theory assumed instead is strictly local in that only adjacent elements and elements in an immediate dominance relation can be part of co...

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.