(the lecture addresses a general audience, no specific knowledge is required)

Abstract. The concept of multiplicity at a point of an algebraic variety stems from very natural topological concepts: branched coverings and covering spaces. The algebraic reformulation of this notion is done in terms of finite field extensions, and finite extensions of rings.

On the other hand, the multiplicity appears, in its algebraic formulation, as a byproduct of an apparently more subtle invariant called the Hilbert Samuel function. This last invariant led to very deep results in algebraic geometry, and shadowed, to some extent, the notion of multiplicity.

As we shall indicate in this talk, the course of research has taken the multiplicity back to the central stage, by showing that it can replace the role of Hilbert Samuel functions in some central aspects of singularity theory.

Ab 15:45 Uhr: Kaffee und Kuchen im Common Room.