Abstract: Given a probability measure mu on the real line, the Christoffel-Darboux (CD) kernel is the kernel of the projection in L^2(mu) onto the subspace of polynomials of degree less than n. As well as playing a fundamental role in random matrix theory, it is extremely useful in the study of the spacings of zeros of the orthogonal polynomials for mu. After discussing some of its basic properties, the talk will review the topics described above, with an emphasis on recent results and open problems.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006