The Probabilistic Method is a powerful tool in tackling many problems in
Combinatorics and it belongs to those areas of mathematical research that have
experienced a most impressive growth in recent years. One of the parts of
discrete mathematics where this approach has proved to be especially useful is
Extremal Combinatorics. In fact, many of the strongest results in this area in
the last few decades are examples of this method.
In this talk we discuss a few recent applications of this methodology. In
particular, we present simple but yet surprisingly powerful probabilistic
arguments which were used recently to make progress on some long-standing
Ramsey and Turan type problems.