<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">(重複で受け取られた方はご容赦ください)<br class="">皆様，<br class=""><br class="">秋田大学の新屋です．<br class=""><br class=""><div class="">以下の要領で3/2(金)に東大にてJacques Sakarovitch先生の講演会が開催されます．</div><div class=""><br class=""></div><div class="">なお，前日(2/28~3/1)の東工大でのSakarovitch先生の連続講演会とは講演内容が別の</div><div class="">新規なものとなっております．どうぞふるってご参加ください．</div><div class=""><div class=""><div class=""><br class="">秋田大学 数理科学コース 新屋良磨 <a href="mailto:ryoma@math.akita-u.ac.jp" class="">ryoma@math.akita-u.ac.jp</a></div><div class=""><br class="">==========</div><div class=""><div class="">Time:</div><div class="">1:30pm, March. 2, 2018</div><div class=""><br class=""><br class=""></div><div class="">Venue:</div><div class="">Room 236, East Building of Department of Chemistry, Faculty of Science(化学東館), University of Tokyo<br class=""><br class=""></div><div class=""><br class=""></div><div class="">Title:</div><div class="">Mysteries and marvels of rational base numeration systems<br class=""><br class="">Jacques Sakarovitch<br class="">CNRS / Paris Diderot University and Telecom ParisTech<br class=""><br class=""><br class="">Abstract:<br class="">The definition of numeration systems with rational base, in a joint<br class="">work with S. Akiyama and Ch. Frougny (Israel J. Math., 2008),<br class="">has allowed to make some progress in a number theoretic problem,<br class="">by means of automata theory and combinatorics of words.<br class="">At the same time, it raised the problem of understanding the<br class="">structure of the sets of the representations of the integers in these<br class="">systems from the point of view of formal language theory.<br class=""><br class="">At first sight, these sets look rather chaotic and do not fit well<br class="">in the classical Chomsky hierarchy of languages. They all enjoy a<br class="">property that makes them defeat, so to speak, any kind of iteration<br class="">lemma. On the other hand, these sets also exhibit remarkable<br class="">regularity properties.<br class=""><br class="">During the recent years, these regularities have been studied in a<br class="">series of joint papers with my student V. Marsault. In particular, we<br class="">have shown that periodic signatures are characteristic of the<br class="">representation languages in rational base numeration systems and<br class="">studied, jointly with S. Akiyama, a kind of autosimilarity property<br class="">that also leads to the construction of Cantor-like sets.<br class=""><br class="">These languages still keep most of their mystery. The partial results<br class="">which will be presented call for further investigations on the subject<br class="">even stronger.</div></div></div><div class="">==========</div></div></body></html>