Recent Progress on Torsion Invariants on Spaces with Isolated Singularities

The Cheeger-Müller theorem identifies analytic torsion with Reidemeister torsion on smooth manifolds. In recent years, significant progress has been made towards extending this correspondence to singular spaces.

In this talk, I will present two approaches to the Cheeger-Müller theorem for spaces with isolated conical singularities. One is based on Witten deformation and Morse-theoretic techniques, while the other relies on intersection Reidemeister torsion, and spectral analysis on singular spaces. I will describe the main ideas of these constructions and compare their respective strengths and limitations.