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.

Recording during the thematic meeting "Harmonic Analysis and Geometric Measure Theory" the October 4, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France)

Filmmaker: Guillaume Hennenfent

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