|Colloquium, 臺南大學應用數學系 吳昌鴻教授|
Thursday, November 2, 16:10—17:00 數學系3174
Title: Surface Geometry and General RelativityDynamics for a Reaction-Diffusion-Advection Problem with Free Boundary
Abstract: We consider a reaction-diffusion-advection logistic model with free boundary in heterogeneous environments. We assume that the species has a tendency to move upward along the resource gradient in addition to random dispersal, and the spreading mechanism of species is determined by a Stefan-type condition. In this setting, we will discuss the effect of advection and resource on the dynamics of the problem. This talk is based on a joint work with Harunori Monobe (Okayama University).
|Colloquium, 哥倫比亞大學數學系、香港中文大學數學系 王慕道教授|
Thursday, November 16, 15:10—16:00 數學系3174
Title: Surface Geometry and General Relativity
Abstract:Many classical results regarding surfaces in 3-dimensional Euclidean space such as Weyl's isometric embedding problem and the Minkowski inequality have their counterparts for surfaces in spacetime. These generalization are not only of mathematical interest, but also of physically relevant importance. They are closely related to fundamental concepts such as gravitational energy and Cosmic censorship. In my talk, I shall discuss some recent developments in these directions.
|Colloquium, 交通大學應用數學系 樂美亨博士|
Thursday, November 16, 16:10—17:00 數學系3174
Title: Surface Parameterization: Theory, Practice, and Application
Abstract:A surface parameterization is a bijective mapping between the surface and a domain of simple shape. It has been widely applied in various fields of image science and engineering. In this talk, I will introduce algorithms for the computation of surface parameterizations, and demonstrate applications to 3D animation and medical images.
|Algebraic Geometry Seminar, 北京清華大學丘成桐數學科學中心 王賜聖研究員|
Friday, November 17, 14:00—15:00 數學系3174
Title: Automorphism and Birational Automorphism Groups of Calabi--Yau Manifolds with Picard Number Two
Calabi-Yau manifolds receive important interest from mathematicians and physicists, not only for the birational geometry but also for the relation with the string theory. In this talk, I will give a brief introduction to Calabi--Yau manifolds and then survey the results of K. Oguiso, V. Lazic and T. Perternell about automorphism and birational automorphism groups of Calabi--Yau manifolds with Picard number two. If time permits, I will discuss three dimensional examples and recent results about Morrison-Kawamata cone conjecture.
|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