this term's topology seminar will be on morse theory and its applications. we'll look first at the basic idea of gradient flow on finite-dimensional manifolds, and how this gives us cell and handle decompositions. then we'll look at the original applications, to geodesics on riemannian manifolds and to bott periodicity. finally we'll look at more modern developments, including perhaps the morse category of a manifold, fukaya's approach to the cup product and massey products, floer homology, circle-valued morse theory and combinatorial morse theory.\\ \noindent as usual this is a learning seminar, where the volunteering participants give talks. at the first meeting i'll give an overview lecture and we'll try to arrange speakers for the rest of term.