Matrix completion is the task of reconstructing missing entries in a matrix of known rank which has gained wide attention through the \$1,000,000 NetFlix prize and the subsequent class action lawsuit.

In the talk I will briefly explain the problem and its many interrelated connections to different fields of mathematics and computer science such as statistics, machine learning, convex optimization, functional analysis, algebraic geometry, commutative algebra, graph theory and combinatorics — highlighting some interesting results and viewpoints which can serve as different but related starting points for approaching the problem of matrix completion.