Illustration as a Mathematical Research Technique / La recherche mathématique par le biais de l'illustration

Collection Illustration as a Mathematical Research Technique / La recherche mathématique par le biais de l'illustration

Organizer(s) Bachman, David ; Coulon, Rémi ; Harriss, Edmund ; Skrodzki, Martin ; Stange, Katherine

Date(s) 05/01/2026 - 09/01/2026

linked URL https://conferences.cirm-math.fr/3491.html

00:00:00 / 00:00:00

4 5

Drawing curves on surfaces or: how I learned to stop worrying and love train-tracks

By Saul Schleimer

Illustration is a vital part of outreach, pedagogy, exposition, and experimentation in mathematics. But illustration also plays a key role in the informal communication between, and within, mathematicians. In low-dimensional topology, certain cartoons of surfaces are used so often that they are essentially part of the Ph.D. syllabus. I'll give an example of how I combined approximately 100 doodles to give a delicate proof by cases, how I fought to remove them, how I failed, and why the doodles did not appear in the final paper.

Information about the video

Date of recording 06/01/2026
Date of publication 20/01/2026
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20432603
Cite this video Schleimer, Saul (06/01/2026). Drawing curves on surfaces or: how I learned to stop worrying and love train-tracks. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20432603
URL https://dx.doi.org/10.24350/CIRM.V.20432603

Domain(s)

Geometric Topology

Bibliography

BELL, Mark C. et SCHLEIMER, Saul. The word problem for the mapping class group in quasi-linear time. arXiv preprint arXiv:2511.02459, 2025. - https://arxiv.org/abs/2511.02459

MSC codes

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