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; 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

2015年5月25日至30日，将在德克萨斯大学奥斯汀分校举行“映射课程组和OUT（F_N）的研讨会”。该会议汇集了研究专家，研究现代几何组理论的两个基石和低维拓扑的基石：映射表面和外部自动化群体的绘制阶级组和外部自动化组。这些群体在整个数学中的无处不在，从许多角度促进了他们的研究，并借鉴了许多不同领域的发展并做出了贡献。该研讨会将举办六个介绍性的迷你课程讲座和世界领先专家的16次研究演讲，描述了尖端技术和该领域的最新结果。 该奖项部分支持讲习班的演讲者和早期的职业数学家。图班级和自由群体的外部自动形态群体在整个漫长而丰富的历史中都伴随着亲密的发展，因为他们的定义和结构有相似之处，并且因为他们在个人元素上具有相同的鲁棒性。 两组之间的不完美类比导致一方面许多惊人的发展，这反过来促使问题在另一方面。 此外，从这些群体的设置中提取思想和技术，导致在许多其他类别的组和几何情况下的应用中进行了概括。 讲座将涵盖各种各样的主题，例如相关复合物的双曲线，准等级嵌入和距离公式，与右角artin组的连接以及其他组的外部自动形态组以及代数和同源性特性，仅等待几个。演讲者和会议参与者将被要求提供与会议有关的主题的链接，该主题将发布到网站：http：//www.math.uiuc.edu/~clein/~clein/modoutsched.html