MaPSS: Maths Postgraduate Seminar Series: Samuel Jelbart -- Geometric Singular Perturbation Theory for Dummies

This talk is intended as an entry level introduction geometric singular perturbation
theory (GSPT), which provides a modern approach to the study of singular perturbation
problems arising in the form of multi-scale dynamical systems in a wide range of
applications.  First and foremost, I aim to show how the ‘singular’ nature of
multi-scale problems manifests itself geometrically, leading naturally to a geometric
framework (and hence the ‘G’ in GSPT).  Once a geometric viewpoint is developed, I
will show by means of a straightforward application how fundamental results with roots
in invariant manifold theory can be applied in order to draw meaningful conclusions
about the dynamics of non-trivial singular systems, without recourse to matched
asymptotics.