Research in surface theory
Supervisor: Dr John Nicholson and Philipp Bader
School: Mathematics & Statistics
Description:
The goal of this project is to work on a research question suitable for a mathematics undergraduate student in the area of mapping class groups of surfaces. The first two or three weeks will be devoted to reading preliminary material about the theory. Afterwards, depending on the student's knowledge and preferences, we will find a concrete problem for the student to work on. One possibility would be working on the action of the mapping class group on the fundamental group or the first homology group of the surface. Another idea is working on pseudo-Anosov theory.
At the end of the project, the student is expected to provide a written document with the summary of everything that he learnt and any problems he solved during the project. It is not expected to prove any original research results. A basic knowledge about algebraic topology and group theory is necessary. No knowledge about mapping class groups is required.