Doorkeeper

Lecture by Prof. Eiko Kin(iTHEMS&AIPMath Joint Seminar)

Mon, 26 Jun 2017 14:00 - 17:00 JST

RIKEN Center for Advanced Intelligence Project (AIP)

Nihonbashi 1-chome Mitsui Building, 15th floor, 1-4-1 Nihonbashi, Chuo-ku, Tokyo 103-0027, Japan

Register

Registration is closed

Get invited to future events

Free admission

Description

Speaker: Eiko Kin (Osaka University, Japan)

Title: Braids and topological mixing

Abstract: In mathematics, the braids are important tools for the knot theory, hyperbolic geometry, and dynamical systems etc. In the last ten years, the braids have been used to study mixing in fluids. Various simple mixing devices (e.g. taffy machines) have been developed. These devices utilize a particular type of braid, so-called a pseudo-Anosov type. The notion of pseudo-Anosov braids comes from the Nielsen-Thurston theory on the surface automorphisms, and the theory says that the devices using pseudo-Anosov braids are ``efficient" in some sense.

In this lecture, I will give a quick introduction of the Nielsen-Thurston theory and the classification of braids. I will give a picture of the ``complexity" forced by pseudo-Anosov braids. In particular, I will explain why pseudo-Anosov braids are useful and why they can be used to build interesting mixing devices.

Reference:
(1) Boyland, Philip L.; Aref, Hassan; Stremler, Mark A.
Topological fluid mechanics of stirring. J. Fluid Mech. 403 (2000), 277–304.

(2) Jean-Luc Thiffeault, A mathematical history of taffy pullers,
preprint

https://arxiv.org/pdf/1608.00152.pdf

Cosponsored by RIKEN iTHEMS and AIP Mathematical Science Team

About this community

RIKEN AIP Public

RIKEN AIP Public

Public events of RIKEN Center for Advanced Intelligence Project (AIP)

Join community