Caltech/USC/UCLA Joint Topology Seminar
One of biggest and most difficult problems in the subject of Gromov-Witten theory is to compute higher genus Gromov-Witten invariants of compact Calabi-Yau 3-fold such as the quintic 3-folds. There have been a collection of remarkable axioms/conjectures from physics (BCOV B-model) regarding the universal structure or axioms of higher genus Gromov-Witten theory of Calabi-Yau 3-folds. In the talk, I will first explain 4 BCOV axioms explicitly for the quintic 3-folds. Then, I will outline a solution for 3+1/2 of them.