PhD Studentship: Group Amalgams

United Kingdom
Jan 12, 2018
Apr 09, 2018
Organization Type
University and College
Full Time

Birmingham University is well-known for its research into finite groups, group geometries, Lie theory and representation theory. The School of Mathematics has a vibrant and productive postgraduate environment that promotes research at the highest level.

Amalgams of collections of finite groups play an pivotal role in finite group theory, groups acting on graphs, group geometries, representation theory and in the study of fusion systems (which itself has applications in homotopy theory). Examples of these manifestations of amalgams appear significantly in the work or the project supervisor, Michael Aschbacher, Marston Conder, Geoff Robinson and Sergey Shpectorov for example. The common theme here is the study of fusion. Fusion in this context means conjugacy in groups. Fusion in a rather complicated way governs how groups are made up from their smaller subgroups. There are many open avenues for novel research in this area. For example the works of Robinson can be extended to other types of amalgams that arise naturally in finite groups. One example that produces exotic results is the Goldschmidt G_5 amalgam represented in odd characteristic which appears to map on to many six-dimensional projective symplectic groups, but in characteristic 3 produces a subgroup Mat (12) the sporadic simple group. One initial problem will be to prove this assertion.


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Funding Notes

This project may be eligible for a college or EPSRC scholarship in competition with all other PhD applications.