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

该项目将为将于2008年7月14-17日在阿默斯特的马萨诸塞大学举行的国际会议“拓扑和几何中的变换群”提供资金。这次会议的与会者来自许多国家。这次会议计划讨论三个主题。第一个是三维流形的对称性。将讨论的主题包括瑟斯顿关于奇集至少为1维的对称的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(在Perelman之后)，以及与纽结和链环有关的3-流形的对称性。第二个主题是4-流形上的群作用。将讨论的主题包括局部线性作用、4-流形上的拓扑作用、4-流形的光滑和辛对称以及规范理论技巧及其在研究4-流形对称性中的作用。第三个主题是高维流形上的变换群。将讨论的主题包括变换群中的同伦理论、群作用与外科理论、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)外，还将邀请相应领域的主要研究人员发表(1小时长)的全体演讲。这些讲座将概述一个特定的研究领域，并提出可能的新研究方向。对称是数学(以及物理)中的一个基本现象，也是一个广泛研究领域的统一主题。这次会议的主要目的是聚集来自不同拓扑和几何领域的研究人员，他们的研究与变换群有关或涉及变换群。这次会议将对年轻的研究人员和研究生特别有用。因为这将使他们有机会更全面地了解各种研究领域，这些领域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.