There is a great demand for the geometric theory of log-concave functions, which can be viewed as the analytic lifting of the geometric theory of convex bodies. Many important results in convex geometry have found their counterparts for log-concave functions.

In this talk, I will explain how to translate terminologies in convex geometry to the geometric theory of log-concave functions, with emphasis on the basic framework for the $L_p$ theory and dual Orlicz theory of log-concave functions. In particular, I will talk about the related Minkowski type problems for log-concave functions.