The MSRC regularly hosts Colloquium talks and research conferences.
- Colloquium talk by Dr Sean Eberhard (MSRC, QUB)
in MAPTC 0G/005 at 16:00 on Monday, 27 November 2023
Title: "Diameter bounds for finite classical groups".
Abstract: "The Cayley graph of a finite group G with respect to a given set of generators X is a graph depicting the "geometry" of the group as determined by X. The diameter of a graph is the greatest distance between two of its points. Strikingly, Cayley graphs of interesting groups tend to be highly connected and have small diameter. I will survey what is known about diameters of simple groups, with particular emphasis on recent positive results on high-rank classical groups such as SL_n(2) due to the speaker and coauthors. The toolkit includes character bounds, probabilistic reasoning, as well as the "trace method", which goes back to Wigner's semicircle law for random matrices."