No abstract uploaded!

Mirror principle is a general method developed in [LLY1]-[LLY4] to compute characteristic classes and characteristic numbers on moduli spaces of stable maps in terms of hypergeometric type series. The counting of the numbers of curves in Calabi-Yau manifolds from mirror symmetry corresponds to the computation of Euler numbers. This principle computes quite general Hirzebruch multiplicative classes such as the total Chern classes.

No abstract uploaded!

Based on the orthogonal Labastida-Mario-Ooguri-Vafa conjecture made by L. Chen and Q. Chen (2012), we derive an infinite product formula for Chern-Simons partition functions, which generalizes Liu and Peng's recent results to the orthogonal case. Symmetry property of this new infinite product structure is also discussed.

We prove that the image of period map is algebraic, as conjectured by Griffiths.