Speaker: Dr. Alan Edelman, Professor of Applied Mathematics, MIT
Abstract: This talk is about random matrix theory. Linear Algebra and maybe a little probability are the only prerequisites. Random matrix theory is now finding many applications. Many more applications remain to be found.
It is truly "matrix statistics," when traditional statistics has been primarily "scalar" and "vector" statistics. The math is so much richer, and the applications to computational finance, HIV research, the Riemann Zeta Function, and crystal growth, to name a few, show how important this area is. I will show some of these applications, and invite you to find some of your own.
For me, there has been an exciting lesson. It has to do with the interplay between mathematics and computation. The computer plays many roles in mathematics. It provides experimental data to suggest, confirm, or discard potential theorems. It provides simulations to bring cold theorems to life. It illustrates in detail the exact nature of particular solutions. Still all of these roles feel like sideshows to the supreme intellectual pursuit of pure mathematics.
For me, random matrix theory has been different. I have found that the last half century or so of mathematical algorithms for numerical linear algebra, forged by the hard constraints of computational efficiency, have given the world even more than a large library of practical algorithms. It has given the world the very essence of linear algebra tools needed to understand random matrix theory. For the first time, I have grown to realize, that even if computational machines had never been built, numerical linear algebra would deserves a special place in pure, yes pure, mathematics.