Diagonally symmetric polynomials and applications

Scope

The diagonally symmetric polynomials are the polynomials in the entries of a matrix of indeterminates that are invariant under the permutations of its columns. They are also known as multisymmetric polynomials, vector symmetric polynomials, MacMahon symmetric polynomials, ...

Diagonally symmetric polynomials were considered at the XIX century by Schläfli and Cayley, and studied with more detail by MacMahon and Junker. They were somehow forgotten afterwards, although many problems were left open. Since 15 years they are rediscovered and important advances in their knowledge were obtained, coming from different communities.

The goal of this conference is to share this knowledge, to present the state-of-the art on this topic, and also to present the problems they need to be solved.

All topics and problem related in a way or another to diagonally symmetric polynomials fit in the scope of the conference. Topic include, but are not limited to:

• Applications in Enumerative Combinatorics
• Diagonal invariants, coinvariants, alternants of the symmetric group.
• Diagonal invariants and coinvariants of other Weyl groups.
• Relations with invariants of several matrices.
• Totally decomposable forms and multiarrangements of hyperplanes.
• Applications in zero-dimensional systems of equations, resultants, eliminants.
• Foulkes' conjecture
• Combinatorial Hopf algebras arising from Colored species
• Symmetric products of varieties

The conference takes place at the CIEM Centro Internacional de Encuentros Matematicos ) at Castro-Urdiales, Spain.