Colloquium DATE 2017-11-23¡@15:10-16:00 PLACE ¼Æ¾ÇÀ]3174±Ð«Ç SPEAKER §õ©v¾§ ³Õ¤h¡]¥xÆW¤j¾Ç¼Æ¾Ç¨t¡^ TITLE Tautological Systems Under the Conifold Transitions on Gr(2,4) ABSTRACT The $B$ model of a Calabi¡XYau manifold were studied by Picard¡XFuchs equations. For Calabi¡XYau hypersurfaces in a projective toric manifold, the GKZ systems, introduced by Gel'fand, Kapranov and Zelevinski, are Picard¡XFuchs 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¡XYau 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.