Symplectic Dynamics/Geometry Seminar

Topic: Inscribing Rectangles in Jordan Loops

Speaker: Rich Schwartz

Affiliation: Brown University

Date & Time: Monday October 14th, 2019, 3:30pm - 4:30pm

Location: Simonyi Hall 101

Video: https://video.ias.edu/sympdyngeo/2019/1017-RichSchwartz

I'll show a graphical user interface I wrote which explores the problem of inscribing rectangles in Jordan loops.  The motivation behind this is the notorious Square Peg Conjecture of Toeplitz, from 1911.I did not manage to solve this problem, but I did get the result that at most 4 points of any Jordan loop are vertices of inscribed  rectangles. I will sketch a proof of this result, mostly through visual demos, and also I will explain two other theorems about inscribed rectangles which at least bear a resemblance to theorems in symplectic geometry.