G. Simmons, Introduction to Topology and Modern Analysis 7. Tensors, manifolds, and vector bundles reviewed. John M. Lee Riemannian Manifolds . We shall discuss various topics of current interest. There are no prerequisites.
All interested persons are welcome.
Some results from remining parts of the book, covered in this semester's MA 651, will be useful, but not crucial for understanding. The basis for this will be the book of M. Auslander, S. Smalo, and I. Reiten, Representation of Artin Algebras , Cambridge Univ. The goal of the course is to give an elementary introduction into singularity theory and its applications to differential equations, wave theory, differential geometry, and control theory. We start with the classification of simple singularities of functions, describe their relation to Coxeter groups generated by reflections. We describe this theory in more details, including recent results on Lagrangian and Legendrian varieties.