## Foundations and Applications

of Random Matrix Theory

### Jacobus Verbaarschot

Stony Brook University, USA

**Friday, 27 October 2006, 13:30**

Lecture room (Sal) F

**Abstract**:

Entropy, Symmetries and Universality are essential concepts in statistical
physics and field theory. They are also at the foundation of Random Matrix
Theory which was introduced by Wigner to describe the statistical
properties of nuclear levels without knowledge of the nuclear Hamiltonian.
Since then, Random Matrix Theories have found applications in many
branches of physics ranging from atomic physics to QCD and quantum gravity
and in mathematics in subjects as varied as the Riemann z-function and
random permutations.
We will review the basic ideas of Random Matrix Theory and explain its
relation to classically chaotic motion. Its successes will be illustrated
by experimental and theoretical results for spectra of a variety of
different physical systems. Recent progress in understanding chiral
symmetry in QCD based on ideas from Random Matrix Theory and the theory of
disordered systems will be discussed. Finally, the concept of universality
is introduced to explain the success of Random Matrix.