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Invariant Theory: Claudio Procesi
Invariant Theory is a part of Mathematics which has known a rather peculiar history.
Its methods and ideas have often merged in other areas of mathematics and more than once its original results have been forgotten, for this it has been compared with the Phoenix, the mythological bird which comes back to life from its ashes.
The reason for this maybe is the following. The idea of invariance, together with that of symmetry, is so basic (not just in Mathematics but in all of Science) that it is unavoidable that ideas connected to it may be deeply transformed as time passes.
Nevertheless there is a more technical way in which we understand Invariant Theory, under this more restricted form it is essentially a discipline at the boundary between algebra and geometry, it concerns essentially the study of actions of algebraic groups upon algebraic varieties and the interplay between the classification of the orbits and that of the invariant functions (or sections).
Of this I will now write.