Thesis supervisor: László Pyber
Location of studies (in Hungarian): Rényi Institute Abbreviation of location of studies: MTA
Description of the research topic:
By a breakthrough result of Harald Helfgott if A is a generating subset of G=PSL(2,q) then AAA is much larger than A or it is equal to G. This theorem has been extended by Pyber-Szabó and by Breuillard-Green-Tao to arbitrary simple groups of Lie type of bounded dimension. The above results have captured the attention of a number of top mathematicians, including four Fields Medalists, Bourgain, Gowers, Lindenstrauss and of course Tao. They have obtained various analogues and extensions of these results to infinite groups and several applications. A major issue is whether there exists some kind of analogue of this result for finite simple groups unbounded dimension. Pyber is presently leading a team of researchers working on this topic, supported by an ERC Advanced Grant. A student could join this team and work on some related problems.
Required language skills: English Further requirements: A good basic understanding of algebra and a definite interest in finite group theory
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