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.

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National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Ricardo Castano-Bernard
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Brown University
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