Speaker: Daniele Dona (HUJI)

Title: Towards a CFSG-free diameter bound for Alt(n).

Abstract: Helfgott and Seress have proved the existence of a quasipolynomial upper bound on the diameter of transitive permutation subgroups: their proof depends on the Classification of Finite Simple Groups through a standard theorem by Cameron. We discuss a potential method to remove CFSG dependence from this result, by using a product-like theorem by Helfgott and a CFSG-free version of Babai's algorithm solving the graph isomorphism problem in order to replace Cameron. The method would lead to a large improvement on the best known CFSG-free diameter bound for Alt(n), proved by Babai in the 1980s, and bring it much closer to Helfgott and Seress.
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