Random Matrix Theory

Random matrix theory is a diverse mathematical tool. It draws together ideas from linear algebra, multivariate calculus, analysis, probability theory, group and representation theory, differential geometry, combinatorics and mathematical physics. It also enjoys a wide number of applications, ranging from wireless communication in engineering, to time series analysis in statistics, quantum chaos and quantum field theory in physics, to the Riemann zeta function zeros and prime numbers in number theory. A self contained development of random matrix theory will be undertaken in this course from various viewpoints.