| 研究実績の概要 |
In FY 2016 I have worked on three different projects. The first one is mirror symmetry for orbifold Calabi-Yau (CY) hypersurfaces. This is a joint work with H. Iritani, Y. Ruan, and Y. Shen, which had continued for several years, but it was completed during FY 2016. We have developed a general framework to study global mirror symmetry. The latter is motivated from physics and consists of transforming Gromov―Witten (GW) invariants into Fan-Jarvis-Ruan-Witten invariants by means of analytic continuation. In particular we proved mirror symmetry for all Fermat CY hypersurfaces. My second project is in fact the basis of my current proposal. I have developed the theory of primitive forms for families of Hurwitz coverings. I also proved that Dubrovin’s primary differentials are primitive forms and established a characterization of the Frobenius manifolds that correspond to an Eynard―Orantin recursion. Finally, the third project is a joint work with V. Tonita. We have proved that the genus-0 K-theoretic GW invariants are governed by an integrable hierarchy of hydrodynamic type.
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