Novikov's problem and tiling billiards | Vidéo | Carmin.tv

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Novikov's problem and tiling billiards

By Olga Paris-Romaskevich

Appears in collection : Differential Geometry, Billiards, and Geometric Optics / Géométrie différentielle, billards et optique géométrique

In the beginning of the 80s, Masur and Veech proved (independently) that a generic interval exchange transformation is uniquely ergodic. At about the same time, on different sides of the iron curtain, Soviet and French mathematicians got interested in the ergodic properties of measured foliations restricted in some parametric classes. Their motivations and constructions were different but the same fractal objet appeared in both. It is called today the Rauzy gasket. The motivation from the Soviet side came from the question asked by Sergei Novikov related to the conductivity theory of monocrystals. His question concerns minimal foliations defined by plane sections of surfaces inside the 3-torus. The Rauzy gasket brings an answer to Novikov's question for a surface of genus 3 with central symmetry and 2 double saddles. Recently, we have obtained a solution of Novikov's problem for any centrally symetric surface of genus 3. This is the most interesting case from the point of view of physical motivations. I will tell some aspects of this story which is based on a series of works, the last and most important one of them is a collaboration with Ivan Dynnikov, Pascal Hubert, Paul Mercat and Alexandra Skripchenko.

Information about the video

Date of recording 05/10/2021
Date of publication 15/11/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19820203
Cite this video Paris-Romaskevich, Olga (05/10/2021). Novikov's problem and tiling billiards. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19820203
URL https://dx.doi.org/10.24350/CIRM.V.19820203

Domain(s)

Bibliography

HUBERT, Pascal et PARIS-ROMASKEVICH, Olga. Triangle tiling billiards and the exceptional family of their escaping trajectories: circumcenters and Rauzy gasket. Experimental Mathematics, 2019, p. 1-30. - https://doi.org/10.1080/10586458.2019.1583615
PARIS-ROMASKEVICH, Olga. Tiling billiards and Dynnikov's helicoid. arXiv preprint arXiv:2102.10201, 2021. - https://arxiv.org/abs/2102.10201
PARIS-ROMASKEVICH, Olga. Trees and flowers on a billiard table. arXiv preprint arXiv:1907.01178, 2019. - https://arxiv.org/abs/1907.01178

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