SAMBa (the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath) has secured funding for a further 5 annual intakes of PhD students.
Read more here: https://samba.ac.uk/exciting-news-for-the-future-of-samba/
SAMBa (the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath) has secured funding for a further 5 annual intakes of PhD students.
Read more here: https://samba.ac.uk/exciting-news-for-the-future-of-samba/
A new CDT in Mathematics for our Future Climate, joint between Imperial, Reading and Southampton Universities, Met Office and more. Further information here.
We show that there exists $C>1$, such that if $A$ is a subset of a non-alternating finite simple group $G$ of density $|A|/|G|= \alpha$, then $AA^{-1}AA^{-1}$ contains a subgroup of density at least $\alpha^{C}$. We will also give a corresponding (slightly weaker) statement for alternating groups.
To prove our results we introduce new hypercontractive inequalities for simple groups. These allow us to show that the (non-abelian) Fourier spectrum of indicators of 'global' sets are concentrated on the high-dimensional irreducible representations. Here globalness is a pseudorandomness notion reminiscent of the notion of spreadness.
The talk is based on joint works with David Ellis, Shai Evra, Guy Kindler, Nathan Lindzey, and Peter Keevash, and Dor Minzer. No prior knowledge of representation theory will be assumed.
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