Daniel Perales, Department of Pure Mathematics, University of Waterloo
"Random matrices, interlacing families of polynomials, and the expected characteristic polynomial"
In this session we will begin by ;reviewing the notion of real stability and some of its basic properties. Then we continue with the study of operators that preserve real stability. For this, we will look into the proof of the Gauss-Lucas Theorem, which asserts that for any complex polynomial f, the roots of its derivative, f', are contained in the convex hull of the roots of f.