Colloquium


DATE2017-11-23 15:10-16:00

PLACE數學館3174教室

SPEAKER李宗儒 博士(台灣大學數學系

TITLE Tautological Systems Under the Conifold Transitions on Gr(2,4)

ABSTRACT The $B$ model of a Calabi—Yau manifold were studied by Picard—Fuchs equations. For Calabi—Yau hypersurfaces in a projective toric manifold, the GKZ systems, introduced by Gel'fand, Kapranov and Zelevinski, are Picard—Fuchs equations. For a projective manifold endowed with a Lie group action, Lian, Song, and Yau introduced a construction of PDE systems, called the tautological system, and showed that this system governs the period integrals of Calabi—Yau complete intersections in the manifold. Via a degeneration of Grassmannian $G(k,n)$ to certain Gorenstein toric Fano varieties $P(k,n)$, we suggest an approach to study the relation between the tautological system on $G(k,n)$ and the extended GKZ system on the small resolution $\widehat P(k,n)$ of $P(k,n)$. We carry out the simplest case $(k,n)=(2,4)$ to ensure its validity and show that the extended GKZ system can be regarded as a tautological system on $\widehat P(2,4)$. In this talk, I will explain these in detail. This is a joint work with Professor Hui-Wen Lin.