Leírás
Abstract:
The diameter of a finite group G is the smallest integer k such that, for every generating set A, every element of G can be written as a product of at most k elements of A. Babai's conjecture states that if G is a finite simple non-abelian group then diam(G) is at most (log|G|)^C for some absolute constant C.
For finite simple groups of Lie type, Breuillard-Green-Tao and Pyber-Szabó showed that C can be taken to depend only on the rank r of G; the function is however huge (a tower of exponentials whose height depends on r). Together with Bajpai and Helfgott, we show that for classical Chevalley groups we can take C=O(r^4*log(r)). Our strategy involves sharp reworking of known techniques that have their roots in algebraic geometry.
In this talk we present the main lines of the proof, and highlight where and how we improve on the path followed by previous papers.
Zoom access:
https://us06web.zoom.us/j/85352565051?pwd=Z2lGSllOcVhyQ2l4bElWNlN2RWtqUT09
Meeting ID: 853 5256 5051
Passcode: 637883