Homotopical Group Theory and Topological Algebraic Geometry, June 2008

该项目将支持参加2008年6月在哥本哈根大学和波恩马克斯普朗克研究所举行的“同调群论和拓扑代数几何”会议。同调群论和拓扑代数几何涉及的相互作用在最高级别的以前遥远的数学领域。它们被一个来自现代同伦理论的共同工具箱捆绑在一起。同调群论揭示了分类空间的结构、群的作用、紧李群的性质和分类等基本问题。它最近显示出对有限单群的分类有新的揭示的潜力。拓扑代数几何汇集了代数几何和同伦理论的思想。它在椭圆上同调和色稳定同伦理论与朗兰兹方案之间的关系等两个领域都取得了重大进展。同调群论和拓扑代数几何是数学的新领域，近年来得到了世界各地研究者的爆炸性发展。由该提案支持的会议将在哥本哈根大学开始，重点是由西北大学的Paul Goerss和圣母大学的Bill Dwyer举办的两个系列讲座，针对初级研究人员。接下来的一周，在马克斯普朗克研究所（Max Planck institute），主要研究人员将报告最新进展。这个想法是将当前的领导者和新的研究人员聚集在一起，并在一个广泛的数学家群体中实现思想的互动和交叉施肥。

This project will support travel to the conference "Homotopical Group Theory and Topological Algebraic Geometry,"at the University of Copenhagen and at the Max Planck Institut in Bonn in June 2008. Homotopical Group Theory and Topological Algebraic Geometry involve the interaction at the highest level of formerly distant areas of mathematics. They are bound together by a common toolbox from modern homotopy theory. Homotopical Group Theory has shed light on fundamental issues such as the structure of classifying spaces and group actions, and the nature and classification of compact Lie groups. It has very recently shown the potential of shedding new light on the classification of finite simple groups. Topological Algebraic Geometry brings together ideas from algebraic geometry and homotopy theory. It has contributed to significant advances in bothareas, including elliptic cohomology and the relationship between the chromatic stable homotopy theory and the Langlands program.Homotopical Group Theory and Topological Algebraic Geometry are new areas of mathematics, and they have recently enjoyed explosive development by researchers around the world. The conference supported by this proposal will begin at the University of Copenhagen, focused on two series of lectures by Paul Goerss of Northwestern University and Bill Dwyer of the University of Notre Dame and aimed at beginning researchers. The following week at the Max Planck Institut, leading researchers will report on the latest developments. The idea is to bring together current leaders and new researchers, and to enable interaction and cross-fertilization of ideas among a broad group of mathematicians.