Homotopy continuation methods for coupled-cluster theory in quantum chemistry

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