Dan Romik, University of California, Davis

Abstract

The moving sofa problem is a well-known open problem in geometry. It asks for the planar shape of largest area that can be moved around a right-angled corner in a two-dimensional hallway of width 1. In this talk I will survey the known results about the problem, which has a surprisingly rich structure, and explain several ways in which its study is informed by experimental mathematics. In particular, I will discuss recent results derived in joint work with Yoav Kallus, in which we developed and implemented an algorithm to prove new upper bounds for the area of a moving sofa shape, improving a 1968 result by Hammersley.