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代数几何与几何分析研讨会

发布时间:2013年11月18日 浏览次数: 文章作者:11-23 发布者:高春玲

代数几何与几何分析研讨会

日程安排:

1122    会议报到

会议地点:海韵实验楼105

 

1123日上午

时间

报告题目

报告人

09:00 – 09:50

Morita equivalence for cyclotomic Birman-Murakami-Wenzl algebras

司梅

上海交通大学

10:00 – 10:50

代数簇分类以及Iitaka 猜想

张磊

陕西师范大学

11:00 – 11:50

Fields, strings and duality

胡智        

中国科学技术大学

 

1123日下午

时间

报告题目

报告人

14:00 – 14:50

从一个初等不等式到代数曲面的奇点

张加劲

四川大学

15:00 – 15:50

Specific Vortex Lines for Gross-Pitaevskii Equation in $R^3$

杨军

深圳大学

16:00 – 16:50

Adams type inequalities with applications in partial differential equations

赵亮

北京师范大学

17:00 – 17:50

A new proof of subcritical Trudinger-Moser inequalities on the whole Euclidean space

朱晓宝

中国人民大学

 

1124日上午

时间

报告题目

报告人

09:00 – 09:50

Delaunay type surfaces along closed geodesic

马世光

南开大学

10:00 – 10:50

Geometric solitons of Hamiltonian flows on manifolds

孙晓伟

中央财经大学

11:00 – 11:50

Teichmueller曲线上的算术

于飞

厦门大学

 

1124日下午

Free discussion.

报告摘要:

 

题目:Morita equivalence for cyclotomic Birman-Murakami-Wenzl algebras 

报告人:司梅         上海交通大学

摘要:In this talk, we give a necessary and sufficient condition on the parameters of cyclotomic BMW 

algebra being singular over an arbitrary field. This gives the Morita equivalence between the 

cyclotomic BMW algebra and the direct sum of some Ariki-koike algebras if the parameters are non-singular over an arbitrary field.

 

题目:代数簇分类以及Iitaka 猜想
报告人:张磊         陕西师范大学
摘要:

我们首先介绍代数簇,双有理分类,典范层,Iitaka 纤维化,Kodaira维数等概念以及代数簇的一种分类原理。然后,我们引入复数域代数簇分类中的几个核心的猜想:极小模型的存在性,aboundance猜想和Iitaka 猜想,我们介绍解释猜想之间的联系和目前的主要进展。接下来我们将介绍关于特征p的代数簇分类的主要进展,以及在推广复数域结果时遇到的问题和困难。最后我们将介绍关于特征p代数簇的Iitaka 猜想的最近的进展。

题目:Fields, strings and duality
报告人:胡智         中国科学技术大学

摘要:

In this talk we introduce  topological field theory, strings, gauge fields, supersymmetry and more. The presentation is more mathematical. BPS states and D-branes are also discussed.

 

题目:从一个初等不等式到代数曲面的奇点
报告人:张加劲     四川大学
摘要:

我们将展示一个初等不等式1/a+1/b+1/c>1与正多面体、SL(2,C)的有限子群、复单李群(Dynkin图)及代数曲面的简单二重奇点的深刻关系。其中SL(2,C)的有限子群与复单李群(Dynkin图)的关系就是著名的(经典)Mckay对应;而SL(n,C)的有限子群与n维商奇点的关系则是现代的Mckay对应的主要研究内容,其中n>3的情形还未知。

 

题目:Specific Vortex Lines for Gross-Pitaevskii Equation in $R^3$

报告人:杨军         深圳大学

摘要:

Quantized vortices have gained major interest in the past few years due to the experimental realization of Bose-Einstein condensates(BEC), a new state of matter predicted by Einstein in 1925 and achieved in 1995. We will talk about the mathematical construction of vortex rings and vortex helices for Gross-Pitaevskii equation from Bose-Einstein condensates.

 

题目:Adams type inequalities with applications in partial differential equations

报告人:赵亮         北京师范大学

摘要:

Using the framework first presented by Ruf and Sani, we prove an Adams type inequality on the whole Euclidean space. As an application of the inequality, we prove a multiplicity result for a singular quasilinear polyharmonic equation .

 

题目:A new proof of subcritical Trudinger-Moser inequalities on the whole Euclidean space

报告人:朱晓宝     中国人民大学

摘要:

In this talk, we give a new proof of subcritical Trudinger-Moser inequality on Rn. All the existing proofs on this inequality are based on the rearrangement argument with respect to functions in the Sobolev space W1,n(Rn). Our method avoids this technique and thus can be used in the Riemannian manifold case and in the entire Heisenberg group.

 

题目:Delaunay type surfaces along closed geodesic

报告人:马世光     南开大学

摘要:

In Euclidean space R^3, there is a kind of constant mean curvature surface called Delaunay surface. It is non compact and periodic. The column can be thought of as a special case of Delaunay surface. In general Riemannian manifolds, if there is a non degenerate closed geodesic, Rafe Mazzeo and Frank Pacard proved that there is a partial foliation of CMC tubes along the geodesic, where the tubes resemble column in Euclidean spaces. I will talk about how to construct CMC surfaces along a non degenerate closed geodesic which resemble Delaunay surface. This is a joint work with Frank Pacard

 

题目:Geometric solitons of Hamiltonian flows on manifolds

报告人:孙晓伟     中央财经大学

摘要:

By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrodinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrodinger flow and geometric KdV flow, including magnetic curves as geometric Schrodinger solitons and explicit geometric KdV solitons on surfaces of revolution

 

题目:Teichmueller曲线上的算术

报告人:于飞         厦门大学

摘要: