Growth in Linear Algebraic Groups and Permutation Groups

Explore a lecture on the mathematical concept of growth in linear algebraic groups and permutation groups, delivered by Harald Andres Helfgott as part of the Hausdorff Trimester Program on Logic and Algorithms in Group Theory. Delve into the study of finite groups and their Cayley graphs, focusing on the diameter of these graphs and its relation to group generators. Examine the long-standing conjecture about the polynomial bound on the diameter of the symmetric group, and learn about the quasipolynomial bound established by Helfgott and Seress in 2011. Gain insights into a simplified version of the proof, highlighting connections with previous research on growth in linear algebraic groups. Reference the related arxiv.org paper for further exploration of this complex mathematical topic.