Semi-galois categories in formal language theory and number theory (浦本武雄氏、東北大学)

2017年   11月 16日 10時 30分 ~ 2017年   11月 17日 12時 00分
浦本武雄 (東北大学)
(1) 2017/11/16 10:30-12:00 (3-210)
(2) 2017/11/16 13:00- (3-210)
(3) 2017/11/17 10:30-12:00 (3-210)

In this talk we introduce our recent work on semi-galois categories. As the name suggests, semi-galois categories are extension of galois categories: While galois categories are dual to profinite groups, semi-galois categories are dual to profinite monoids. Originally, we introduced this class of categories in order to axiomatize a certain branch in formal language theory of computer science, known as Eilenberg theory, which concerns a systematic classification of regular languages, finite monoids, and deterministic finite automata; but recently observed that semi-galois categories are inherently related to class field theory as well. In this talk, (1) starting from a background of semi-galois categories and motivation in formal language theory, (2) we introduce the axiom, basic general properties and examples of semi-galois categories, and then (3) discuss an arithmetic (or F_1) analogue of a classical theorem known as Christol's theorem (an automata-theoretic characterization of when a formal power series over finite field is algebraic over the polynomial ring F_q[t]) and its natural relation to semi-galois categories.

DGS Seminar 003