Title: Gromov--Witten invariants of orbifold projective lines and quasi-modular forms

Speaker: Prof. Todor Milanov, Institute for the Physics and Mathematics of the Universe, University of Tokyo

Time: 2011.06.03, Friday, 9:00-10:00 am

Place: Resource Building 1328

Abstract: In a joint work with Y. Ruan, together with a companion work of his students M. Krawitz and Y. Schen, we prove the LG/CY correspondence for simple elliptic singularities. The LG/CY conjecture in general says that there is an identification between two different theories: the so called Fan--Jarvis--Ruan theory defined for certain classes of weighted-homogeneous polynomials W and the Gromov--Witten theory of a certain CY manifold defined by the equation W=0. Our method is based on the Givental's quantization formalism and Saito's theory of primitive forms. In particular, we managed to prove that the GW invariants of the CY manifold are quasi-modular forms.