Research-Geometry & Topology Seminar

Automatic sequences and the link with number theory and algebraicity in positive characteristics

Abstract

We will give an introduction to automatic sequences and the link with number theory and algebraicity in positive characteristics. We will aboard the following topics:

1. Definition and Examples

We give classical examples of automatic sequences that arise naturally from

the study of various problems in different domains of mathematics.

We then give the definition via automata. We state and prove

Kleene's Theorem which asserts that every regular language is accepted by some deterministic finite automaton and vice versa.

2. Basic Properties

We give basic properties of automatic sequences, including two Theorems

of Cobham, the Pumping Lemma, and closure properties.

Schedule:

16:20-18:10, Apr 20, 22, 27, 29 and May 6, 11