ncku-talk2017-11-23

Colloquium

DATE 2017-11-23　15:10-16:00

PLACE 數學館3174教室

SPEAKER 李宗儒博士（台灣大學）

TITLE Introduction to Tautological Systems

ABSTRACT The B model of a Calabi–Yau manifold were studied by Picard–Fuchs equa- tions. Given a toric manifold, Gel’fand, Kapranov and Zelevinski introduced a PDE system which governs the period integrals of Calabi–Yau 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–Yau complete intersections in the manifold [LSY13, LY13]. This construction also gives rise to a kind of generalized GKZ system for Calabi–Yau 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.

Colloquium

DATE	2017-11-23　15:10-16:00

PLACE	數學館3174教室

SPEAKER	李宗儒博士（台灣大學）

TITLE	Introduction to Tautological Systems

ABSTRACT	The B model of a Calabi–Yau manifold were studied by Picard–Fuchs equa- tions. Given a toric manifold, Gel’fand, Kapranov and Zelevinski introduced a PDE system which governs the period integrals of Calabi–Yau 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–Yau complete intersections in the manifold [LSY13, LY13]. This construction also gives rise to a kind of generalized GKZ system for Calabi–Yau 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.