The Ricci flow is a geometric differential equation which recently made headlines for its key role in the proof
of the Poincaré Conjecture (a century-old mathematical conjecture whose resolution carried a $1,000,000
prize). Developing the theory of boundary-value problems for the Ricci flow is a fundamental question, which
has remained open for over two decades. The present project aims to answer this question on a wide class
of spaces, along with the closely related question of solvability of boundary-value problems for the
prescribed Ricci curvature equation. The results will have ramifications in a variety of fields, from pure
mathematics to quantum field theory, relativity and modelling of biological systems.