Marko Stošić "Matrix completions and combinatorics of polynomial paths"

In this talk we will present some of the matrix completion problems and how their solutions have been obtained trough history. In particular, we shall focus on the role of polynomial paths of invariant factors of the involved matrices and how their internal combinatorics has an effect on the completion problems. We shall start by presenting some of the classical combinatorial results involving interlacing inequality and convexity of polynomial paths, and end with a recent vast generalisation of such combinatorial properties. In addition, these results have huge potential of applications in general completion problems.

This is joint work with M. Dodig

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