京都大学数理解析研究所の佐藤です。

12月1日11:00から、オークランド大学のBakh Khoussainov先生と 京都大学数理解析研究所の滝坂透氏の両名に以下のjoint talkを していただくことになりましたので、ご連絡いたします。 どうぞお気軽にお越しください。

========== Time: 11:00-12:00, 1 Dec, 2016 Place: Rm 478, Research Building 2, Main Campus, Kyoto University 京都大学 本部構内 総合研究2号館 4階478号室 http://www.kyoto-u.ac.jp/en/access/yoshida/main.html (Building 34) http://www.kyoto-u.ac.jp/ja/access/campus/map6r_y.htm (34番の建物)

Speakers: Bakh Khoussainov (University of Auckland) and Toru Takisaka (RIMS, Kyoto university)

Title: On large scale geometries of infinite strings

Abstract: Motivated by notions in geometric group theory, we introduce the concept of large scale geometry on infinite strings.

Informally, two infinite strings have the same large scale geometry if there is a bi-Lipschitz map between both strings with a finite uniform distortion. We call these maps quasi-isometric maps.

Introduction of large scale geometries poses several questions. The first question is related to understanding the partial order induced by quasi-isometric maps on large scale geometries of strings. We prove that there is the greatest large scale geometry and infinitely many minimal large scale geometries. The second is related to understanding the quasi-isometric maps on various classes of strings. The third question address the issue of building quasi-isometric maps between computable infinite strings. We show that the problem is Sigma_3-complete. The fourth question is about understanding sets of large scale geometries given some tools (e.g. Buchi automata) that describe sets of strings. We provide an efficient algorithm that gives a full description of large scale geometries of strings accepted by such automata. Finally, the fifth question asks if it is possible to associate with every large scale geometry an algebraic structure that describes the geometry uniquely. Here we use tools of geometric group theory by invoking the notion of asymptotic cone.