We parameterize the geometry of an industrial aeroengine combustor using Free Form Deformation (FFD). We then define the thermoacoustic system parameters and impose the acoustic boundary conditions to calculate the thermoacoustic eigenmode of the model using an open source parallelized Helmholtz solver. We then use adjoint methods to calculate the shape derivatives of the unstable eigenvalue with respect to the shape parameters. First we calculate the sensitivities with respect to surface movements. Second, we calculate the sensitivities with respect to the FFD control points. We modify the FFD control point positions in order to reduce the thermoacoustic growth rate until the mode considered is stable. These findings show how, when combined with other constraints, this method could be used to reduce combustion instability in industrial annular combustors through geometric modifications.