Transformation Groups in Topology and Geometry, July 14-17, 2008

该项目将为2008年7月14日至17日在阿默斯特的马萨诸塞州大学举行的“拓扑和几何变换组”国际会议提供资金。这次会议的与会者来自许多国家。会议计划包括三个主题。首先是三维流形的对称性。讨论的主题包括Thurston关于奇异集维数至少为1的对称的3-流形的几何化的猜想，具有有限基本群的3-流形的几何化（Perelman之后），以及与纽结和链环有关的3-流形的对称性。内容包括局部线性、四维流形上的拓扑作用、四维流形的光滑和辛对称、规范理论及其在四维流形对称性研究中的作用;第三个主题是高维流形上的变换群，内容包括变换群中的同伦理论、群作用和外科手术理论、辛几何中的群作用、以及代数簇上的群作用。除了标准的会议演讲（30分钟），还将邀请相应领域的领先研究人员进行全体会议演讲（1小时）。这些讲座将给出一个给定的研究领域的概述，并提出可能的新的研究方向。对称性是数学（以及物理学）中的一个基本现象，这是一个广泛的研究领域的统一主题。这次会议的主要目的是汇集来自拓扑和几何的研究人员，他们的研究与变换群有关或涉及变换群。这次会议对年轻的研究人员和研究生特别有用。因为这将给他们一个机会，以获得一个更全面和全面的看法，各种研究领域，只是在表面上看起来是脱节和无关的。

This project is to provide funding for the international conference ``Transformation Groups in Topology and Geometry'', which will take place at the University of Massachusetts in Amherst, July 14-17, 2008. The participants of this conference come from many countries. The conference plans to cover three subjects. The first is symmetries of 3-dimensional manifolds. The topics to be discussed include Thurston's Conjecture of geometrization of 3-manifoldswith symmetries whose singular set is of dimension at least 1, geometrization (after Perelman) of 3-manifolds with finite fundamental groups, and symmetries of 3-manifolds related to knots and links.A second topic is group actions on 4-manifolds. The topics to be discussed include locally linear, topological actions on 4-manifolds, smooth and symplectic symmetries of 4-manifolds, and gauge theoretic techniques and their roles in studying symmetries of 4-manifolds.A third subject is transformation groups on higher dimensional manifolds.The topics to be discussed include homotopy theory in transformation groups, group actions and surgery theory, group actions in symplectic geometry, and group actions on algebraic varieties. Besides the standard conference talks (30 minutes long) there will be invited (1-hour long) plenary talks delivered by leading researchers in the corresponding areas. These talks will give an overview of a given research area and suggest possible new research directions.Symmetry is a fundamental phenomenon in mathematics (as well as physics),which is a unifying theme of a wide range of research areas.The main purpose of this conference is to bring together researchers from quite diverse areas of topology and geometry whose research is related to or involves transformation groups. This conference will be especially useful to young researchers and graduate students. For it will give them a chance to obtain a more global and comprehensive view of various research areas which only on a surface look to be disjoint and unrelated.