** "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 (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 \(\exp(O(n(\log n)^3))\).