Conference: Ramification in algebra and geometry

这笔资金支持将于2011年5月16日至20日在埃默里大学举行的“代数和几何中的分支”会议。这次会议主要集中在下列数学领域内代数、几何和数论之间的相互作用：线性代数群和齐次空间的算术、上同调不变量、本质维度、除法代数和Brauer群、Chow群和Motivic分解、一般Galois扩张和Brauer-Manin障碍。这次会议汇集了在这些领域工作的国际专家和初级研究人员。统一的主题是分支。任何见过螺杆(螺旋面)的人都熟悉分支的几何概念：沿着螺杆的长度看，中心轴--所有的线在那里相遇--就是螺杆被分叉的地方。在中心轴之外，螺丝没有分叉：穿过平行于中心轴的螺纹的激光束只穿透不同的金属片。在这里，分叉区分螺杆(螺旋面)和弹簧(螺旋面)。这一概念的抽象在许多数学领域中已被证明是基本的；这次会议将集中在代数和几何中的一些最近的应用。

This grant provides support for the conference "Ramification inAlgebra and Geometry" to be held at Emory University, 16-20 May 2011.This conference is primarily focused on the interaction betweenalgebra, geometry, and number theory within the following thematicareas: the arithmetic of linear algebraic groups and homogeneousspaces, cohomological invariants, essential dimension, divisionalgebras and the Brauer group, Chow groups and motivic decomposition,generic Galois extensions, and Brauer-Manin obstructions.This conference brings together international experts and juniorresearchers working in these areas. The unifying theme isramification. The geometric notion of ramification is familiar toanyone who has seen a screw (helicoid): looking along the length of ascrew, the central axis--where all the threads meet--is where thescrew is "ramified." Off the central axis, the screw is not ramified:a laser beam passing through the threads parallel to the central axispierces only distinct sheets of metal. Here, the ramificationdistinguishes a screw (helicoid) from a spring (helix). Abstractionsof this concept have proved fundamental in many areas of mathematics;this conference will focus on some of the recent applications inalgebra and geometry.