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

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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.