The Topology of Algebraic Varieties

2012年9月24日至28日将在蒙特利尔举办“代数变种的拓扑学”研讨会，随后将于2012年9月21日至23日举办三个相关的小型课程。关于正规代数簇的简单拓扑不变量和其他自然不变量之间的联系，特别是来自二次曲面和仿射代数几何的自然不变量之间的联系，可以在以下website:http://www.crm.umontreal.ca/2012/Topology12/index_e.phpThis中找到更多信息。主要主题将包括有理连通簇的简单连通性，通过循环空间理论对Shafarevich映射的相关发展，以及通过各种伪装通过Hodge理论解决光滑簇(具有线性基本群)的万能覆盖上的Shafarevich猜想。在其他中心学科中，将有关于曲面奇点的管道理论的最新进展，这些理论连接了许多关于带纽结的代数簇和3-流形理论的经典问题，以及关于奇异簇的(或)陈数的Bogomolov-Miyaoka-Yau不等式在仿射代数几何中的几个新的突破结果中的关键作用。会议将聚集代数/解析几何的专家以及在低维复奇点理论工作的相关拓扑学家，在国际范围内进行卓有成效的信息交换和互动。它将向新一代研究人员介绍在这一领域使用的现代拓扑和分析工具。

A workshop on "The Topology of Algebraic Varieties" will be held in Montreal from September 24 to 28, 2012 preceded by three related mini-courses from September 21 to 23, 2012. Additional information can be found at the following website:http://www.crm.umontreal.ca/2012/Topology12/index_e.phpThis is a workshop on connections between simple topological invariants of a normal algebraic variety, and other natural invariants, especially those coming from birational and affine algebraic geometry. Major themes will include the simple connectedness of rationally connected varieties, the related development of the Shafarevich map via cycle space theory, and the resolution of the Shafarevich conjecture on the universal cover of a smooth variety (with linear fundamental group) via Hodge theory in various guises. Among other central subjects there will be recent advances in the theory of plumbing for surface singularities that bridged many classical problems on algebraic varieties with knots and the theory of 3-manifolds, and the key role of the Bogomolov-Miyaoka-Yau inequality on (orbifold) Chern numbers of singular varieties in several new break-through results in affine algebraic geometry.The conference will bring together experts in algebraic/analytic geometry as well as relevant topologists working in low dimensional complex singularity theory for fruitful exchange of information and interaction on an international scale. It will introduce modern topological and analytical tools used in this area to a new generation of researchers.