Speaker: John Robertson
Talk Title: Distributions, Differential Forms, Sheaf Cohomology, & Dynamical Systems
Abstract: We use a variety of mathematical tools to find new invariant objects for self maps of compact manifolds. We combine self maps of compact anifolds with short exact sequences of sheaves to get a long exact cohomology sequence with an induced self map. That long exact sequence has different rates of expansion on different members of the long exact sequence. Some terms of our long exact sequence are finite dimensional, and thus have nice features like igenvectors and eigvenvalues. We use these nice features of finite dimensional vectors spaces to find invariant objects in other members of the long exact sequence. The objects we find come from analysis, and generalize both submanifolds and differential forms. Our results use a very general etup which allows us to derive results simultaneously for holomorphic and real dynamical systems. While the proofs use tools from analysis and sheaf cohomology, the results are easy to visualize.
Refreshments will be served from 3:30-4:00 p.m. in 294 TMCB.