"The aim of this project is to provide a comparison result between analytic and topological torsion in the presence of singularities. Comparison theorems between analytic and topological torsion on smooth manifolds have been an object of intensive study during the last 40 years in Mathematics. More recently, the study of analytic torsion on singular spaces has gained interest. It is therefore natural to look for its topological counterpart, i.e. the right object on the topological side of the comparison. The idea of this project is to approach the question using the Witten deformation. This approach in the singular context is new and is based on the generalisation of the Witten deformation to singular spaces obtained by the applicant in a series of papers.Ursula Ludwig, the researcher of the proposal, is an expert in the geometry, topology and analysis of singular spaces. Jean-Michel Bismut, the scientist in charge, is one of the world leading experts in local index techniques and questions of analytic and topological torsion. The problem of comparing torsions for singular spaces will be addressed in this project by joining these two competences."