Workshop on mapping class groups of surfaces and outer automorphism groups of free groups

曲面类群映射和自由群外自同构群研讨会

• 批准号: 1542752
• 负责人: Alan Reid
• 金额: $ 3万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-06-15 至 2016-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1542752&HistoricalAwards=false
• 关键词: Workshop; mapping; class; groups; surfaces

The "Workshop on Mapping Class Groups and Out(F_N)" will be held at the University of Texas, Austin, May 25-30, 2015. This conference brings together experts studying two of the cornerstones of modern geometric group theory and low-dimensional topology: mapping class groups of surfaces and outer automorphism groups of free groups. The ubiquity of these groups throughout mathematics has motivated their study from many perspectives, drawing on and contributing to the development of numerous diverse fields. The workshop will feature six introductory mini-course lectures and 16 research talks by the world's leading experts, describing cutting edge techniques and the latest results in the field. This award partially supports workshop speakers and early career mathematicians.Mapping class groups and outer automorphism groups of free groups have evolved hand-in-hand throughout their long and rich history because of the similarities in their definitions and structure, and because they share much of the same robustness in their individual elements. The imperfect analogy between the two groups has led to many striking developments on one side, which in turn motivate problems on the other. In addition, abstracting the ideas and techniques from the setting of these groups has led to generalizations with applications in many other classes of groups and geometric situations. The lectures will cover a wide array of topics, such as hyperbolicity of associated complexes, quasi-isometric embeddings and distance formulas, connections to right-angled Artin groups and to outer automorphism group of other groups, and algebraic and homological properties, to name a few. Speakers and conference participants will be asked to provide links to topics related to the conference, which will be posted to the website: http://www.math.uiuc.edu/~clein/modoutsched.html

“映射类群和出（F_N）研讨会”将于 2015 年 5 月 25 日至 30 日在德克萨斯大学奥斯汀分校举行。这次会议汇集了研究现代几何群论和低维群论两大基石的专家。拓扑：映射面的类群和自由群的外自同构群。这些群体在数学中的普遍存在激发了他们从多个角度进行研究，借鉴并促进了许多不同领域的发展。该研讨会将由世界领先的专家举办 6 场介绍性迷你课程讲座和 16 场研究讲座，介绍该领域的前沿技术和最新成果。 该奖项部分支持研讨会演讲者和早期职业数学家。映射类群和自由群的外自同构群在其漫长而丰富的历史中携手并进，因为它们的定义和结构相似，并且因为它们有很多共同点它们的各个元素具有相同的稳健性。 这两个群体之间不完美的类比导致一方面出现了许多引人注目的发展，而另一方面又引发了问题。 此外，从这些群的设置中抽象出思想和技术已经导致了在许多其他类别的群和几何情况中的应用的概括。 讲座将涵盖广泛的主题，例如相关复形的双曲性、拟等距嵌入和距离公式、与直角 Artin 群和其他群的外自同构群的联系，以及代数和同调性质，等等。很少。演讲者和会议参与者将被要求提供与会议相关的主题的链接，这些链接将发布到网站：http://www.math.uiuc.edu/~clein/modoutsched.html