Colloquium DATE 2017-11-23¡@15:10-16:00 PLACE ¼Æ¾ÇÀ]3174±Ð«Ç SPEAKER §õ©v¾§ ³Õ¤h¡]¥xÆW¤j¾Ç¡^ TITLE Introduction to Tautological Systems ABSTRACT The B model of a Calabi¡VYau manifold were studied by Picard¡VFuchs equa- tions. Given a toric manifold, Gel¡¦fand, Kapranov and Zelevinski introduced a PDE system which governs the period integrals of Calabi¡VYau hypersur- faces in it, known as the GKZ system. For a projective manifold endowed with a Lie group action, Lian, Song, and Yau also introduced a construction of PDE systems, called the tautological system, and showed that this system gov- erns the period integrals of Calabi¡VYau complete intersections in the manifold [LSY13, LY13]. This construction also gives rise to a kind of generalized GKZ system for Calabi¡VYau hypersurfaces in a toric manifold when the Lie group is taken to be the full automorphism group of the toric manifold and it can be shown that this system coincides with the extended GKZ system introduced in [HKTY95, HLY96], [LL16]. In this talk, I will explain their construction and give some explicit examples.