Colloquium Series Seminar

In 1911, Toeplitz asked whether every Jordan curve in the plane contains the vertices of a square. Toeplitz's question is still open, but it has given rise to many interesting variations and partial results. I will survey some of these and steer towards a recent result of mine with Andrew Lobb: every smooth Jordan curve in the plane contains the vertices of a cyclic quadrilateral of any orientation-preserving similarity class. The argument involves symplectic geometry in a surprising way. Speaker(s): Joshua Greene (Boston College)