Wednesday, April 5 2017 - Thursday, April 6 2017
11:30 - 13:00

 * 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 thelast part of the lectures I gave at IMSc on Automatic sequences. However, this setof lectures is self-contained: no \emph{a priori} knowledge of automatic sequencesis 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 $\mathbb{Q}$-linearlyindependent, then $X$ is ultimately periodic.In lecture 1, we recall definitions and basic facts about automatic sequences and wepresent a result on Diophantine approximation.In lecture 2, we show that a sequence satisfying the hypothesis of Cobham’s theoremis 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