Kleinian Schottky groups, Patterson-Sullivan measures, and Fourier decay

We will start with the notion of Fourier dimension of a subset of $\mathbb{R}^d$. We will then focus on the particular case of the limit sets of Kleinian Schottky groups and the asymptotic behavior of the Fourier transform of the Patterson-Sullivan measures. We will discuss the connection with the resonance theory on hyperbolic manifolds and random walks on $SL_2(\mathbb{C})$. This is a joint work with Jialun Li and Frédéric Naud.