9313048 Daverman A good deal of effort has gone into the recognition problem for topological manifolds. This is the problem of finding effective criteria for distinguishing manifolds from other, more singular, geometric objects. The classical implicit function theorem gives one such criterion, but even when this fails and the functions describing the geometric object have singularities, the object itself may nevertheless be a manifold. A compelling example of this phenomenon is the celebrated Cannon-Edwards theorem, which says that the double suspension of an homology sphere is a sphere. In 1978, Cannon proposed a simple set of criteria for recognizing high- dimensional topological manifolds. In 1991, Bryant, Ferry, Mio, and Weinberger showed that Cannon's criteria were insufficient. In fact, they constructed infinitely many distinct families of "noncartesian manifolds" - manifold-like objects satisfying Cannon's criteria which do not have local coordinate descriptions. The detailed geometry of these spaces is mysterious. The purpose of the proposed conference is to expose this work to the mathematical public and seek applications of these ideas both within geometric topology and in other areas of mathematics and mathematical physics. The conference will be very appealing throughout the Southeastern United States, a region which boasts a long tradition of interest in the topic. ***
