Seminar by Prof.Jean-Pierre Eckmann "Rolling stones reveal new structures in SO(3)"

<Date>
October 7 (Tue), 2025
14:00-15:00 Seminar
15:00-15:20 Q&A

<Speaker>
Prof.Jean-Pierre Eckmann, Professor Emeritus, University of Geneva

<Title>
Rolling stones reveal new structures in SO(3)

<Abstract>
This project started with the question whether one can construct a specially formed stone so that it rolls along a prescribed curve and its repetitions. We then discovered that for almost all given paths
this is indeed possible, but, astonishingly, one needs to traverse TWO copies of the prescribed line to regain the original orientation of the stone. We finally discovered how this result is related to stochastic and Diophantine properties of rotations in SO(3) and SU(2). (This is work with Tsvi Tlusty and Yaroslav Sobolev)

J-P Eckmann
Département de Physique Théorique
and
Section de Mathématiques
Université de Genève

References
Y.I. Sobolev, R. Dong, T. Tlusty, J.-P. Eckmann, S. Granick,
and B.A. Grzybowski, Solid-body trajectoids shaped to  roll
along desired pathways, Nature,  620, 310 (2023)

J.-P. Eckmann, Y.I. Sobolev, and T. Tlusty, Tumbling downhill along a
given curve, Notices of the American Mathematical Society, 71 (2024)

J.-P. Eckmann, T. Tlusty, Walks in Rotation Spaces Return Home When
Doubled and Scaled, PRL, in print

https://www.youtube.com/watch?v=Ub8EdBv5xxU

https://www.youtube.com/watch?v=fUYWZUP_r5Y