## Multisymmetric polynomials and applications in algebra.

### Emmanuel Briand, (Universidad de Cantabria, Spain).

The multisymmetric polynomials are the diagonal invariants of the
symmetric group. We will present some problems about these objects:
presentation of their algebra by generators and relations and
Foulkes-Howe conjecture. We will discuss the direct applications in
algebra: isomorphism between the symmetric product and the Chow
variety of multisets of points of the projective space, study of
systems of polynomial equations in with finitely many solutions,
charactacterization of the polynomials (in several variables) that
factorize totally (i.-e. as products of polynomials of degree 1).

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