Commuting nilpotent matrices
Anthony Iarrobino

Abstract: We consider the nilpotent commutator N_B of an nXn matrix B in Jordan form of partition P: N_B is all nilpotent matrices commuting with B. The problem of what Jordan forms (partitions Q) may occur for matrices A in N_B, and even what is the "generic" Jordan form Q(P) that occurs for most A in N_B is open. We discuss this problem, including recent work by Oblak and Koszir, Basili and I, and others on it, and related open questions.