|Colloquium, 臺灣大學數學系 李宗儒博士|
Thursday, November 23, 15:10—16:00 數學系3174
Title: Tautological Systems Under the Conifold Transitions on Gr(2,4)
Abstract:The 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.
|Colloquium, 臺灣大學數學系 沈俊嚴教授|
Thursday, November 23, 16:10—17:00 數學系3174
Title: Nonhomogeneous Harmonic Analysis
Abstract:One of the major open problems in nonhomogeneous Harmonic analysis is to find the necessary and sufficient conditions for the boundedness of two weights inequality for singular integrals. In this talk, we will first discuss the famous two weights problem for the Hilbert transform and outline our proof that settles this longstanding open problem. We then discuss some of the main difficulties for higher dimensional singular integrals. Some of the important applications to other fields will be also discussed, in particular an application of our T1 theorem for the Cauchy transform in the complex plane settles the open problem: the embedding problem for the model spaces.
|Colloquium, 保德信壽險顧問 林思成先生|
Thursday, November 30, 15:00—17:00 總圖書館B1國際會議廳