Inverse problem for a time-dependent convection-diffusion equation in admissible geometries

We consider a partial data inverse problem for time-dependent convection-diffusion equation on an admissible manifold. We prove that the time-dependent convection term can be recovered uniquely modulo a gauge invariance while the time-dependent potential can be recovered fully. There has been several works on inverse problems related to the steady state Convection-diffusion operator in Euclidean as well as in Riemannian geometry however inverse problems related to time-dependent Convection-diffusion equation on manifold is not studied in the prior works which is the main objective of this paper. In fact to the best of our information, the problem considered here is the first work related to a partial data inverse problem for recovering both first and zeroth order time-dependent perturbartions of evolution equations in Riemannian geometry.