A gentle introduction to the geometry and dynamics of bicycle tracks
时间  Datetime
2025-10-27 14:00 — 18:00
地点  Venue
会议室(706)
报告人  Speaker
Gil Bor
单位  Affiliation
CIMAT, Guanajuato, Mexico (墨西哥国家数学研究中心瓜纳华托)
报告摘要  Abstract

A simple model of  bicycle motion consists of an oriented segment of fixed length moving in the plane in such a way that it is always tangent to the generated back track (the "no-slip condition"). If the front track is prescribed, the trajectory of the rear wheel is uniquely determined by this condition, once the initial orientation of the bicycle is chosen, via a certain Ricatti-type first order differential equation.  This model has attracted much attention in recent years, due in part to its unexpected relations with other mathematical problems, old and new: hyperbolic geometry, Euler's elastica, completely integrable curve evolution (the filament equation). In this mini-course I will describe these relations and some open problems and conjectures.
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FROM 202.120.11.*