The variational bicomplex and Takens’ theorem


Slides of the talk here.

Abstract: All of mathematical physics either concerns infinitesimal descriptions of reality or global descriptions of reality. A simple example of the former is a differential equation, whereas fields like gravitational fields and electromagnetic fields exemplify the latter. Differential Geometry and Differential Topology provide a language that unfiies this description in the language of bundles. For instance, fields are defined as sections of appropriate bundles. In fact, a field theory, which is usually formalised as a variational calculus problem and its leading differential equation, can be prescribed in terms of special bundles called jet bundles. This formalism for field theory spans both classical and quantum field theory, after suitable modifications.