"Geometry and Analysis on Groups" Research Seminar



Time: 2017.11.14, 15:15–17:00
Location: Seminarraum 9, Oskar-Morgenstern-Platz 1, 2.Stock
Title: "On the diameter problem for finite simple groups."
Speaker: Arindam Biswas (Universitšt Wien)
Abstract: If \(G\) is a non-abelian finite simple group and \(S\) an arbitrary symmetric generating set, it is conjectured that its Cayley graph \(C(G; S)\) will have a diameter bound of \((\log |G|)^{O(1)}\). The talk will highlight some of the recent progress in this direction and show a non-trivial upper bound when \(G\) is a finite simple Lie group of large rank. Specifically we shall show that if \(G\) has rank \(n\), and its base field has bounded size, then the diameter of \(C(G; S)\) would be bounded by \(\exp(O(n(\log n)^3))\).