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“同伦群理论和拓扑代数几何”会议的旅费。同伦群理论和拓扑代数几何涉及在以前遥远的数学领域的最高水平上的相互作用。它们被现代同伦理论中的一个公共工具箱捆绑在一起。同伦群理论揭示了诸如分类空间和群作用的结构、紧李群的性质和分类等基本问题。它最近显示出在有限单群的分类上有新的曙光的潜力。拓扑代数几何融合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程序之间的关系等两个领域都取得了显著的进展。同伦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的研究人员的爆炸性发展。这一提议支持的会议将在哥本哈根大学开始，重点是西北大学的Paul Goerss和圣母大学的Bill Dwyer的两个系列讲座，旨在培养初级研究人员。下周，在马克斯·普朗克研究所，领先的研究人员将报告最新的发展。这一想法是为了将现有的领导者和新的研究人员聚集在一起，并使广泛的数学家群体之间能够进行思想的互动和交叉培养。

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.