UG Colloquium
Topic: The Contact Geometry of 1-Jet Bundles
Speaker: Ruslan Erdnigor
Date: February 13, 2025
Location: BA6183 (seminar room)
Abstract
Jet bundles are objects that provide a very geometric treatment of partial differential equations, allowing to understand such things as (higher) symmetries and conserved currents on a conceptual level. I will define the bundle of 1-jets of functions on a smooth manifold, as well as the Cartan distribution on the total space of that bundle, and, as a particular application, explain how the contact form defining the Cartan distribution provides a geometric way of finding and describing local solutions to first-order partial differential equations in full generality.
