Christopher Sinclair
MATHEMATICS COLLOQUIUM
Speaker: Christopher Sinclair Abstract. Consider an ensemble (set) of square matrices equipped with a probability measure. Associated to each matrix is a set of eigenvalues, and the probability measure on matrices induces a probability measure on all such sets of eigenvalues. Random matrix theory is the study of this induced measure, what it tells us about the statistics of eigenvalues of matrices in our ensemble, and the application of these statistics to other areas. As we will see, eigenvalues of random matrices repel each other, and this property is useful for modeling other sequences of numbers: critical zeros of zeta functions and energy levels of atomic spectra being the standard examples. In this talk I will explain how, for many classical ensemble, the induced measure on eigenvalues yields a determinantal or Pfaffian point process on sets of eigenvalues, the implications of this, and a new connection with the world of hyperpfaffians. |