Daniel Perales, Department of Pure Mathematics, University of Waterloo
"Random matrices, interlacing families of polynomials, and the expected characteristic polynomial"
In this learning seminar we will study some techniques pertaining to expected characteristic polynomials of random matrices, which were developed and were found to have a variety of strong applications in a sequence of recent papers by Marcus, Spielman and Srivastava. Some specific topics that we will look at include: basic results about expected characteristic polynomials, the 'interlacing families' technique, and the theory of real stable polynomials.
The first meeting of the learning seminar, on October 25, will be devoted to introducing the notion of interlacing family of polynomials, and to proving a few basic facts concerning this notion.
M3 3103