Linear algebra, commuting varieties and Hilbert schemes (R. Basili, A. Conca, T. Košir)

We will discuss problems that arise when studying pairs or triples of commuting matrices. For instance, a number of authors recently discussed the question of description of the dense orbit in the nilpotent commutator of a given nilpotent matrix (Panyushev, Basili and Iarrobino, Košir and Oblak), and also more general question of describing all possible pairs of Jordan partitions for a pair of commuting nilpotent matrix. Since the participants of the workshop are coming from various backgrounds, we expect to discuss these and other problems of commuting matrices from many aspects, e.g. of linear algebra, commutative algebra, algebraic geometry, Lie theory, and combinatorics.