Mapping Class Groups and Teichmuller Theory, May 7-14, 2014

映射类组和 Teichmuller 理论，2014 年 5 月 7-14 日

• 批准号: 1439369
• 负责人: Jeffrey Brock
• 金额: $ 3万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-05-01 至 2015-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1439369&HistoricalAwards=false
• 关键词: Mapping; Class; Groups; Teichmuller; Theory

The conference Mapping Class Groups and Teichmuller Theory - in Ramat Hanadiv, Israel, May 7-14, 2014 will make possible the participation of a large number of early career mathematicians at an important conference to assess the state of the field and build new connections between mathematicians in the areas of geometry and topology. An important area in geometry is the study of the range of all possible shapes a given type of geometric object can take. For example, one might study the range of all possible shapes of triangles, circles, or other kinds of geometric objects. Teichmüller theory takes as its objects 2-dimensional surfaces, and studies the shapes of these surfaces. When a shape is symmetric, these symmetries are recorded by an algebraic notion called the "mapping class group". From topology, to geometry, to physics, the interaction of these notions continues to produce new fruitful topics of study. Indeed Teichmüller space (the "space of shapes") has its own geometry, and symmetries of the shapes appear as symmetries of Teichmüller space. This conference will seek to introduce new researchers to emerging aspects and connections in this burgeoning field.The study of mapping class groups and Teichmüller theory lies at the intersection of a variety of important mathematical topics, including geometry, topology, geometric group theory, and representation theory. New research threads in these different subject areas have emerged recently, and the time is right to revisit the connections between such topics to assess parallels between their development. While there are few mathematicians in Israel that work directly in the subject, there is a larger group of mathematicians that work in closely related areas, and great opportunity for enhancing connections between these working groups and those that exist elsewhere. The proposed conference on Mapping Class Groups and Teichmüller Theory, in Ramat Hanadiv, Israel, will provide a unique and new opportunity for scholars from a broad range of career stages to meet in Israel and interact with Israeli mathematicians in related areas, and will serve to broaden the geographic and intellectual base of the field.Conference URL: http://www.math.technion.ac.il/cms/decade_2011-2020/year_2013-2014/mapping/

会议地图班级组和Teichmuller理论 - 在以色列的拉马特·汉纳迪夫（Ramat Hanadiv），2014年5月7日至14日，将使许多早期职业数学家在一项重要的会议上参与评估该领域的状态并在几何学和拓扑领域建立新的数学家之间的新联系。几何学的一个重要区域是对给定类型的几何对象所采取的所有可能形状范围的研究。例如，人们可能会研究三角形，电路或其他类型的几何对象的所有可能形状的范围。 Teichmüller理论将其作为其对象的二维表面，并研究这些表面的形状。当形状对称时，这些对称是由称为“映射类组”的代数概念记录的。从拓扑到几何学，再到物理学，这些音符的相互作用继续产生新的富有成果的研究主题。的确，Teichmüller空间（“形状的空间”）具有自己的几何形状，形状的对称性显示为Teichmüller空间的对称性。这次会议将旨在向新研究人员介绍这个水伤领域的新兴方面和联系。映射课程组和Teichmüller理论的研究在于各种重要的数学主题的交集，包括几何，拓扑，几何群体理论和代表理论。这些不同主题领域的新研究线程最近出现了，现在是时候重新审视此类主题之间的联系以评估其发展之间的相似之处了。虽然以色列中很少有数学家直接在这个主题中工作，但有一群在相关领域工作的数学家群体很大，这是加强这些工作组与存在其他地方的数学家的绝佳机会。在以色列拉马特·汉纳迪夫（Ramat Hanadiv）举行的有关阶级阶级团体和Teichmüller理论的拟议会议将为来自各种职业阶段的学者提供一个独特而新的机会，以在以色列见面并与以色列的数学家互动，并将拓宽领域的地理和知识基础。 http://www.math.technion.ac.il/cms/decade_2011-2020/year_2013-2014/mapping/