The main focus of this program will be on the interaction between 3-dimensional Hyperbolic Geometry and Holomorphic Dynamics. These two fields have flourished through the past 30 years, with numerous fruitful exchanges that have enriched both of them. In recent years, we have witnessed many exciting breakthroughs in the both fields. The program would provide an opportunity to reckon the recent achievements and to discuss further directions they open. Along with the above two main themes, we plan to incorporate into the program a number of related directions, including the theory of laminations, partially hyperbolic dynamics, and flows on moduli spaces. All of them are closely interconnected, in particular, through the theory of laminations which provides them with a unifying framework. Tentatively, the beginning of the program will concentrate on topics in partially hyperbolic dynamics, Teichmüller flow, and laminations, the middle part will focus on one- and two-dimensional holomorphic dynamics; and the end will cover various topics in hyperbolic geometry including the recent solution of longstanding conjectures in deformation theory of hyperbolic manifolds and recent advances in Thurston's Geometrization Program. Accordingly, the program will include two or three workshops and a number of graduate courses and mini-courses on the topics of the program.
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The Fields Institute, Toronto, Canada
Fall 2005 - Spring 2006