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Banach Algebras on Grigorchuk’s Group

Grigorchuk’s group is a certain group of automorphisms of the binary rooted tree, first introduced by Rostislav Grigorchuk in 1980. The group is remarkable for resolving a number of famous questions in group theory. For instance, it was the first example of a finitely-generated group of intermediate growth. In this talk we outline how certain Beurling algebras on Grigorchuk’s group answer two questions in the theory of Banach algebras: one concerning the theory of left ideals in Banach algebras, the second concerning the second dual of l¹(G) with Arens multiplication.