45 years on: Some Abstract Mathematics of Eilenberg

Martin Hyland
Thursday, July 25, 2013 - from 09:30 to 10:30
Samuel Eilenberg had a distinctive taste for abstract mathematics which extended beyond his famous contributions to algebraic topology and homological algebra. In this talk I shall discuss how Eilenberg's taste manifested itself in some of his other work. I shall consider in particular the book Recursiveness written with Calvin Elgot and the paper Automata in General Algebras joint with Jesse Wright. In the first of these the theory of recursive functions is developed using subcategories of the category of relations. The basic setting is of the free monoid of words on a finite alphabet. The second presents an approach to automata with a very contemporary flavour. I shall sketch the main mathematical ideas and attempt to place them in the context of more recent developments.