CIRM Workshop: Representations of Surface Groups

PIS将于2008年9月1-5日在国际照明数学中心组织一次研讨会，主题是基本曲面群的表示。会议将围绕以下主题组织：(1)Teichmueller空间上的Hitchin联系，共形场理论，以及映射类群的有限维么正表示；(2)Teichmueller理论的正几何和热带几何，Fock和Goncharov意义下的高等Teichmueller-thurston理论；(3)通过簇代数产生的映射类群的无限维表示；(4)全纯微分的平移面和模空间；(5)双曲几何和三维洛伦兹共形几何。这一学科近年来非常活跃，与数学物理、低维拓扑、动力系统、表示论和代数几何有许多联系。这次会议是在相关领域的几次会议之后举行的，尽管这次会议的重点略有不同。PI希望将来自不同领域和世界许多不同地区的研究人员聚集在一起。这次会议的形式将受到美国数学研究所的启发，去年在那里举办了一个相关的研讨会。

The PIs are organizing a workshop at the Centre International de Rencontres Mathematiques in Luminy, September 1-5, 2008 on the subject of Representations of fundamental groups of surfaces.The conference will be organized around minicourses, covering the following topics:(1) Hitchin's connection over Teichmueller spaces, conformal field theory, and the finite dimensional unitary representations of the mapping class group;(2) Positive and tropical geometry of Teichmueller theory, higher Teichmueller-Thurston theory in the sense of Fock and Goncharov;(3) Infinite-dimensional representations of mapping class groups arising through cluster algebras;(4) Translation surfaces and moduli spaces of holomorphic quadratic differentials;(5) Hyperbolic geometry and 3-dimensional Lorentzian conformal geometry.This subject has been extremely active in recent years, with many connections opening up with mathematical physics, low-dimensional topology, dynamical systems, representation theory and algebraic geometry. This conference follows several conferences in related fields, although this one has a somewhat different focus. The PIs hope to bring together researchers from different fields, and many different parts of the world. The format of this conference will be inspired by that of the American Institute of Mathematics where a related workshop was held last year.