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MA469 Fourth Year Research Project.

Lieven Le Bruyn has been blogging about representations of subgroups of the modular group. Here are the relevant pages listed in the order in which they were posted. These groups are important and geometrical. The representations of these groups are studied using path algebras.
  • Hexagonal Moonshine
  • The Dedekind tessellation
  • Modular quilts and cuboid tree diagrams
  • Hyperbolic Mathieu polygons
  • Farey codes
  • Hexagonal moonshine
  • Generators of modular groups
  • Hexagonal Moonshine
  • There are (at least) two possible projects. One project would be based on the geometry and group theory. The idea would be to take the ideas which have been presented in these posting in an informal style and to present them in a more coherent and scholarly style. The other project is more ambitious. Lieven is an expert on the representation theory and so he does not discuss his approach here as he already understands it. The project would then give the statements of some general results and then show how they applied in these examples.
    This is a project for Fourth Year MMath students.

    Series of Lie groups

    The focus of my research is on the idea of series of Lie groups. Here are the slides from a talk.