| * Venue | Media Centre |
| * Speaker | J-M. Deshouillers |
| * Title | Cobham’s theorem |
| Affiliation | University of Bordeaux |
| Abstract | These three lectures present a proof of Cobham’s theorem stated below. They represent the last part of the lectures I gave at IMSc on Automatic sequences. However, this set of lectures is self-contained: no \emph{a priori} knowledge of automatic sequences is required. Cobham’s theorem states that if an infinite set $X$ of integers is both $k$ and $\ell$ automatic, where $\log k$ and $\log \ell$ are $\mathbb{Q}$-linearly independent, then $X$ is ultimately periodic. In lecture 1, we recall definitions and basic facts about automatic sequences and we present a result on Diophantine approximation. In lecture 2, we show that a sequence satisfying the hypothesis of Cobham’s theorem is syndetic, i.e. the difference between its consecutive terms is bounded. In lecture 3, we end the proof of Cobham’s theorem. |
| * Announcement? | Public |
| * Refreshments? | Before the event |
| * Honorarium? | None |
| Special Arrangements? | Videography |
| * Host name and email |