MPhil / PhD Studentship (Mathematics) - On the product decomposition conjecture

This programme of research is within the study of finite group theory (although some investigation of linear algebraic groups may also be involved). The aim is to prove, or partially prove, the Product Decomposition Conjecture which concerns “conjugate-growth” of subsets of a finite simple group: roughly speaking, given a finite nonabelian simple group G and a subset A in G of size at least 2, we would like to show that one can always write G as a product of “not many” conjugates of A.

This notion of conjugate-growth has interesting connections to many interesting areas of mathematics, including expander graphs, the product growth results of Helfgott et al, bases of permutation groups, word problems and more.

In the process of working on this conjecture, the student can expect to learn a great deal about the structure of finite simple groups (especially the simple classical groups) and, in particular, will study and make use of one of the most famous theorems in mathematics, the Classification of Finite Simple Groups.

Applicants should have a minimum of an upper second class honours degree in Mathematics and / or a good Masters’ degree.

Applicants are not expected to submit a research proposal for this studentship. Please select MPhil/PhD (Computing/Maths) when applying.

Closing date for applications is Monday 15th February 2016 and the studentship will commence April 2016.