In algebraic topology, generalized cohomology theories have become a powerful tool for translating topological problems into algebraic problems, where one can expect to do calculations. The more algebraic structure one can extract, the better. The last 30 years or so have seen extensive development of the family of complex-oriented cohomology theories, which allow one to tap into the existing rich algebraic machinery of formal group laws. Applications include many profound results in topology. However, much of the work has taken place at a rather small number of centers, and the proposed 4-day conference is intended to disseminate the present state of the field to a wider audience, including publication of the proceedings of the conference.
Topology is the study of those properties of geometric objects such as spheres, tori and other surfaces, and higher-dimensional analogues, that do not depend on such concepts as distance and angle. A stock example is that a donut is treated as equivalent to a coffee mug, as one can be deformed into the other, without tearing or gluing, if they are plastic enough, but not equivalent to a cup without a handle, as the hole will not go away. Algebraic topology seeks to convert topological problems into algebraic problems that one can solve. One powerful modern tool is the concept of a complex-oriented cohomology theory, which is the focus of the proposed 4-day conference. This conference is intended to disseminate the present state of the field and its results more widely.
