In this talk, I will attempt to review some of the results of Oleg Lepski and his co-authors that influenced the course of mathematical statistics over the last thirty years.
It is hard to do fair justice to the origins of ideas that circulate among a vast community of scientists, and instead of taking the route of an illegitimate historian, I will follow byways and give a personal account of what I know and understand of Oleg's influence and personality. In particular I will try not to talk too much about "Lepski's method", but rather focus on others of his many contributions.[-]

In the talk I will discuss rationality criteria for Fano 3-folds of geometric Picard number 1 over a non-closed field $k$ of characteristic 0. Among these there are 8 types of geometrically rational varieties. We prove that in one of these cases any variety of this type is k-rational, in four cases the criterion of rationality is the existence of a $k$-rational point, and in the last three cases the criterion is the existence of a $k$-rational point and a k rational curve of genus 0 and degree 1, 2, and 3 respectively. The last result is based on recent results of Benoist-Wittenberg. This is a joint work with Yuri Prokhorov.[-]