Extreme value statistics: An overview and perspectives

Extreme value statistics (EVS) concerns the study of the statistics of the
maximum or the minimum of a set of random variables. This is an important
problem for any time-series and has applications in climate, finance,
sports, all the way to physics of disordered systems where one is
typically interested in the statistics of the ground state energy. While the EVS
of `uncorrelated' variables is well understood, not much is known for strongly
correlated random variables. Only recently this subject has gained much
importance both in statistical physics and in probability theory. In this
talk, I will give an overview of the developments in physics and mathematics.
In particular, I will discuss some recent developements on the EVS of
strongly correlated systems and discuss several examples.