In-Person Talk

In 1911, Otto Toeplitz conjectured that every Jordan curve in the plane inscribes a square. 110 years later, the Square Peg Problem is solved only in special cases e.g., for smooth curves. It is natural to ask whether Jordan curves inscribe more general quadrilaterals as well.

Last year, Joshua Green and Andrew Lobb proved that every smooth Jordan curve inscribes every cyclic quadrilateral. Their proof combines an old result of Euclid and a more recent result of Viterbo and Polterovich on embedded Lagrangian tori in $\mathbb{C}^2$.