In this introductory-level talk, I will present the main
work of my thesis: the question of stability of the Vlasov-Maxwell
System. This system, which describes the time evolution of plasma, is
of significant interest for physicists, both since much of the
universe is made up of plasma, and since there are many industrial
applications involving plasmas. Moreover, the question of stability is
of special interest to those attempting to construct fusion reactors.
After exploring the basic mathematical and physical ideas, we will
find a simple criterion that guarantees linear instability, and we
will give concrete examples where it is satisfied.