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 (Universität 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 $$\exp(O(n(\log n)^3))$$.