[geometry-ml:06245] 5月の東大数理談話会のご案内

[Yoshiki Oshima]

幾何学メーリングリストの皆様

東京大学大学院数理科学研究科における５月の談話会についてご案内申し上げます．

日時：５月３０日（金）１５：３０～１６：３０

場所：東京大学大学院数理科学研究科大講義室（対面のみ）
https://www.ms.u-tokyo.ac.jp/access/

講演者：John A G Roberts 氏
(UNSW Sydney/東京大学大学院数理科学研究科)

題目：
Arithmetic and geometric aspects of the (symbolic) dynamics of piecewise-linear maps

摘要：
We study a family of planar area-preserving maps, described by different SL(2,R) matrices on the right and left half-planes. Such maps, studied extensively by Lagarias and Rains in 2005, can support periodic and quasiperiodic dynamics with a foliation of the plane by invariant curves. The parameter space is two dimensional (the parameters being the traces of the two matrices) and the set of parameters for which an initial condition on the half-plane boundary returns to it are algebraic “critical” curves, described by the symbolic dynamics of the itinerary between the boundaries. An important component of the planar dynamics is the rotational dynamics it induces on the unit circle. The study of the arithmetic, algebraic, and geometric aspects of the planar and circle (symbolic) dynamics has connections to various parts of number theory and geometry, which I will mention.  These include: Farey sequences; continued fraction expansions and continuant polynomials; the character variety of group representations in SL(2, C) and PSL(2, C); and the group of polynomial diffeomorphisms of C^3 preserving the Fricke-Vogt invariant x^2 + y^2 + z^2 - xyz.
This is joint work with Asaki Saito (Hakodate) and Franco Vivaldi (London).

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2025年度談話会委員
会田茂樹，大島芳樹，志甫淳（委員長），高田了

なお，談話会・数理科学講演会の情報は，下記のウェブサイトに掲載されております．
https://www.ms.u-tokyo.ac.jp/seminar/colloquium/