Suggestions of projects related to this course:

students are welcome to suggest their own topics

  • Applications of Singularity Theory to Differential Geometry
We see a simple example of this in the lectures. Suitable for any level and any length project.
  • Applications of Singularity Theory to bifurcation problems
  • Classification of singularities
  • Milnor fibration
If \(f:(\mathbb{C}^n,0)\to\mathbb{C}\) is a germ of a holomorphic function with an isolated critical point, then a beautiful theorem of Milnor relates the codimension of the critical point to the geometry/topology of the fibres \(f^{-1}(t)\) for \(t\neq 0\).
  • Singularities with symmetry
Right- or contact-equivalence can be be adapted to take care of functions/maps with symmetry.
  • General Singularity Theory Equivalences
As discussed in the course, there are many different possible equivalences of maps, and the aim of the project would be to investigate these.
  • The preparation theorem
This is an important theorem which underlies the "versal unfolding theorem". The project would consist of understanding the proof, which is a combination of algebra and analysis, writing it up, and then looking at a few applications (eg to the versal unfolding theorem). Suitable for Level 4 or an MSc dissertation. But be warned: it's a hard proof!