The Witten deformation on a smooth compact manifold is an analytic proof of the Morse
inequalities, which has been proposed by Witten in the 80s and is inspired from ideas in quantum
field theory. The Witten deformation is one of the main actors in the extension by Bismut and Zhang
of the comparison between analytic and topological torsion of a smooth compact manifold, aka the
The aim of this talk is to explain how to extend the Witten deformation to singular spaces with
conical singularities and radial Morse functions, and how this can be used to achieve a Cheeger-Müller
theorem for these spaces.