Georgia Institute of Technology College of Sciences

A real matrix is called orthostochastic if it is the entrywise square of an orthogonal matrix. These matrices have been shown to be deeply connected to determinantal representations of polynomials, and also arise naturally in physics. However, the equations defining the real variety are known only up to the 3x3 case. I will show how various techniques of numerical algebraic geometry give a way of finding (set-theoretic) defining equations for the 4x4 orthostochastic variety, which are smaller (both in number and degree) than the naive equations one might initially guess. Based on joint work with Papri Dey.