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The GROGandGIN project investigates growth patterns in mathematical groups, focusing on random walks and their implications in group theory and number theory. By exploring probabilistic techniques, the project aims to advance understanding of growth in both matrix and permutation groups.
In recent years there has been spectacular progress in studying growth in groups. A central result in this new area, obtained by Pyber-Szabo' (with a similar result proved by Breuillard-Green-Tao), shows that powers of generating subsets of finite simple groups of ""bounded dimension"" grow fast.
Extending this Product Theorem Szabo' and the PI also proved a weaker version of a conjecture of Helfgott-Lindenstrauss.
The Product Theorem has deep consequences in the study of groups, number theory a…
HUN-REN ALFRED RENYI INSTITUTE OF MATHEMATICS
HUN-REN RENYI ALFRED MATEMATIKAI KUTATOINTEZET
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