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An integration approach to the Toeplitz square peg problem
Post-edited
Authors : Tao, Terence (Author of the conference)
CIRM (Publisher )
55N45 - Products and intersections
CIRM (Publisher )
Abstract :
The Toeplitz square peg problem asks if every simple closed curve in the plane inscribes a square. This is known for sufficiently regular curves (e.g. polygons), but is open in general. We show that the answer is affirmative if the curve consists of two Lipschitz graphs of constant less than 1 using an integration by parts technique, and give some related problems which look more tractable.
MSC Codes : 55N45 - Products and intersections
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 06/10/2017 Conference Date : 04/10/2017 Series : The Fields Medallists Subseries : Research talks arXiv category : General Topology ; Combinatorics Mathematical Area(s) : Topology ; Combinatorics Format : MP4 (.mp4) - HD Video Time : 00:58:43 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-10-04_Tao.mp4 
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Information on the Event
Event Title : Harmonic analysis and geometric measure theory / Analyse harmonique et théorie géométrique de la mesureEvent Organizers : Bernicot, Frédéric ; Durand-Cartagena, Estibalitz ; Lemenant, Antoine ; Pajot, Hervé ; Rigot, Séverine Dates : 02/10/2017 - 06/10/2017 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1685.html
Citation Data
DOI : 10.24350/CIRM.V.19226703Cite this video as: Tao, Terence (2017). An integration approach to the Toeplitz square peg problem. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19226703 URI : http://dx.doi.org/10.24350/CIRM.V.19226703 |
See Also
- [Multi angle] Ill-posedness for Leray solutions of the ipodissipative Navier-Stokes equations / Author of the conference De Lellis, Camillo.
- [Multi angle] Localization of eigenfunctions via an effective potential / Author of the conference Jerison, David.
- [Multi angle] 30 years of $T(b)$ theorems / Author of the conference Auscher, Pascal.
- [Multi angle] Parametrizing with Guy / Author of the conference Toro, Tatiana.
Bibliography
- Matschke, B. (2014). A survey on the square peg problem, Notices of the American Mathematical Society, 61(4), 346-352 - http://dx.doi.org/10.1090/noti1100
- Tao, T. (2017). An integration approach to the Toeplitz square peg problem.
- Toeplitz, 0. (1911). Ueber einige Aufgaben der Analysis situs. In Verhandlungen der schweizerischen naturforschenden Gesellschaft. 94. Jahresversammlung vom 30. Juli bis 2. August 1911 in Solothurn (p. 197). Aarau: H. R. Sauerländer - https://archive.org/stream/verhandlungender1911schw#page/n7/mode/2up
