Homotopy continuation methods for coupled-cluster theory in quantum chemistry

Homotopy methods have proven to be a powerful tool for understanding the multitude of solu-tions provided by the coupled-cluster polynomial equations. This endeavour has been pioneered byquantum chemists that have undertaken both elaborate numerical as well as mathematical investi-gations. Recently, from the perspective of applied mathematics, new interest in these approacheshas emerged using both topological degree theory and algebraically oriented tools. This articleprovides an overview of describing the latter development.