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

2014年5月7日至14日在以色列拉马特哈纳迪夫举行的会议“映射类群和Teichmuller理论”将使大量早期职业数学家有可能参加一次重要的会议，以评估该领域的现状，并在几何和拓扑领域的数学家之间建立新的联系。几何中的一个重要领域是研究给定几何对象的所有可能形状的范围。例如，人们可以研究三角形、圆形或其他几何物体的所有可能形状的范围。teichmller理论以二维曲面为研究对象，研究这些曲面的形状。当一个形状是对称的，这些对称性被一个称为“映射类群”的代数概念记录下来。从拓扑学到几何学，再到物理学，这些概念的相互作用不断产生新的富有成果的研究课题。事实上，teichmller空间（“形状空间”）有自己的几何形状，形状的对称性表现为teichmller空间的对称性。本次会议将寻求向新研究人员介绍这一新兴领域的新兴方面和联系。映射类群和teichm<s:1> ller理论的研究是许多重要数学课题的交叉点，包括几何、拓扑、几何群论和表示理论。最近在这些不同的学科领域出现了新的研究线索，现在是时候重新审视这些主题之间的联系，以评估它们发展之间的相似之处。虽然以色列很少有数学家直接从事这一领域的工作，但有更多的数学家在密切相关的领域工作，并且有很大的机会加强这些工作组与其他地方存在的工作组之间的联系。拟议在以色列拉马特哈纳迪夫举行的关于绘图类组和teichm<s:1> ller理论的会议将为来自不同职业阶段的学者在以色列会面并与相关领域的以色列数学家互动提供一个独特的新机会，并将有助于扩大该领域的地理和知识基础。会议网址：http://www.math.technion.ac.il/cms/decade_2011-2020/year_2013-2014/mapping/

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/