### Top Eigenvalue of a Random Matrix

Satya Majumdar, Paris

The statistical properties of the top eigenvalue of a
random matrix are of interest in diverse fields ranging from
disordered systems to statistical data analysis and even in string theory.
In this talk I'll
discuss some recent developments in the theory of extremely
rare fluctuations (large deviations) of the largest eigenvalue
using a Coulomb gas method. Various other applications of this
Coulomb gas method will also be discussed.