Knots, Möbius bands, and inscribed rectangles

Does every Jordan curve in the Euclidean plane contain 4 points that form the corners of a square?
Starting from this old metric problem posed by Toeplitz a hundred years ago, we discuss problems in low-dimensional topology.
The talk will feature knots---embedded circles in 3-dimensional space---and
disks and Möbius bands knotted in 4-dimensional space.
No prior knowledge of low-dimensional Topology will be assumed.