What are solutions to O(P)DEs?

Abstract: In this talk, I will (try to) give a (soft) introduction to the geometric theory of differential equations. This theory makes rigorous sense of multivalued solutions to both ordinary and partial differential equations, which serve as an alternative to weak solutions developed in the functional analytic framework. This is the only theory (I am aware of) that formulates precise sufficient conditions for integrability of general type ODEs (sort of “Galois theory” for ODEs) in terms properties of their symmetry group. This result is known as the Lie-Bianchi theorem. Its particular case is the celebrated Liouville-Arnold theorem on integrability of Hamiltonian systems. If time permits (likely, not), we will also see applications of this theory in different areas: hydrodynamics, Monge-Ampère equations, classification problems in algebra.

Mathematics

Audience: general audience

Gothenburg PhD seminar

Series comments: Rooms and times may vary, please check the latest update. In-person only.