Research Projects

The project aims to address the rational dilation problem for distinguished varieties in families of domains like polydiscs and symmetrized polydiscs. The goal is to find a model for commuting operator tuples associated with a compact subset of Cn in terms of commuting normal operator tuples associated with the distinguished boundary of the compact set. This is particularly challenging for polynomially convex domains like polydiscs or symmetrized polydiscs. An algebraic variety is distinguished with respect to a domain if it intersects and exits the domain through the distinguished boundary without touching any other parts of its topological boundary. The project aims to determine if rational dilation succeeds on a distinguished variety in a polydomain and its connection with the Nevanlinna-Pick interpolation problem.