Abstract: A geometric study of ODEs brings additional tools and looks at properties that are independent of coordinate-changes, thus attempts to characterize ODEs that are equivalent to the familiar ones. In the case of my PhD project, I consider the geometrization of systems of 2nd order ODEs into generalized path geometries, and study the latter with its corresponding parabolic geometries. This correspondence brings some instant observations; more importantly, it associates to each object a collection of canonical geometric tools, on which there are further constraints from Lie representation theories.
In this talk I will explain what generalized path geometries are and how they are related to systems of 2nd order ODEs, then loosely show what the corresponding parabolic geometries are and how one could implement them.
Generalized path geometries - studying systems of 2nd order ODEs with parabolic geometries
06.04.2022 15:00 - 15:45
Organiser:
Vienna School of Mathematics
Location:
Sky Lounge, 12. OG, OMP 1
Location:
und online