**Bayesian nonparametric approach to log-concave density estimation**

In the beginning of the talk I will give a (somewhat) lengthier introduction to Bayesian nonparametric methods. Then I will focus on estimating log-concave densities on R, which is a canonical problem in the area of shape-constrained nonparametric inference. We present a Bayesian nonparametric approach to this problem based on an exponentiated Dirichlet process mixture prior and show that the posterior distribution converges to the log-concave truth at the (near-) minimax rate in Hellinger distance.