Iwasawa algebras

Billy Woods (University of Glasgow)

Wednesday 8th November, 2017 16:00-17:00 Maths 311B


Iwasawa algebras - that is, completed group rings of certain profinite groups - were named for their origins in a series of papers by Kenkichi Iwasawa in the 1960s. By studying the algebraic properties of the simplest of these rings, Iwasawa was able to understand the asymptotic behaviour of class numbers in certain infinite extensions of number fields. They (and related rings) have since continued to arise as important objects of study in modern number-theoretic contexts. I'll briefly outline some of this history and motivation; but then I'll quickly move away from the number theory, and spend the rest of the time talking about some of what's known about the algebraic properties of Iwasawa algebras.

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