Topology is concerned with the intrinsic properties of shapes of spaces. One class of spaces which plays a central role in mathematics, and whose topology is extensively studied, are the n dimensional manifolds. These are spaces which locally look like Euclidean n-dimensional space.<br>Historically, topology has been a nexus point where algebraic geometry, differential geometry and partial differential equations meet and influence each other, influence topology, and are influenced by topology. More recently, topology and differential geometry have provided the language in which to formulate much of modern theoretical high energy physics. This interaction has brought topology, and mathematics more generally, a whole host of new questions and ideas. Because of its central place in a broad spectrum of mathematics there has always been a great deal of interaction between work in topology and work in these neighboring disciplines. That is true of the topology group at Columbia, which has enjoyed a close connection with the algebraic geometry group, the geometric PDE group, and the mathematical physics group at Columbia. In addition to close connection to the other research groups, our topology group also enjoys close collaboration with the symplectic geometers at Stony Brook and Courant, running a thrice-per-semester joint symplectic geometry seminar.