Abstract: We consider performing inference about the location of the mode of a log-concave density on $\mathbb{R}$. Log-concave densities are always unimodal, and the mode is a natural parameter of interest. In nonparametric settings, the location of the maximum of a function is generally not estimable at a $\sqrt{n}$-rate and does not always have a normal limiting distribution. Current methods for testing or forming confidence intervals for the mode of a density are generally complicated and perform poorly. We thus study a tuning parameter free shape-constrained likelihood ratio test, which can be inverted to form confidence intervals, for the mode. This is joint work with Jon Wellner.