The author was arrested under the name of crimes of count-revolution by the socialist public security bureau when he was only 9 years old. He was tortured brutally almost to death while the authority just wanted to force his father to admit his so called guilty. The author did not yield to the authority and was put in jail unjustly for safeguarding his father…
Gromov-Witten theory started as an attempt to provide a rigorous mathematical foundation for the so-called A-model topological string theory of Calabi-Yau varieties. Even though it can be defined for all the Kähler/symplectic manifolds, the theory on Calabi-Yau varieties remains the most difficult one. In fact, a great deal of techniques were developed for non-Calabi-Yau varieties during the last twenty years. These techniques have only limited bearing on the Calabi-Yau cases. In a certain sense, Calabi-Yau cases are very special too. There are two outstanding problems for the Gromov-Witten theory of Calabi-Yau varieties and they are the focus of our investigation.
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