## Introduction to Projective Structures and Opers, course by Peter Dalakov

A complex projective structure on a Riemann surface is determined by an atlas, whose transition functions are Moebius (fractional-linear) transformations. There are multiple descriptions of these structures: as certain flat PGL_2-bundles, as Sturm-Liouville operators, as holomorphic connections on the (first) jet bundle of the dual of a theta-characteristic, etc. This mini-course is an introduction to the fundamentals of projective structures, accessible to students and non-specialists. We will also explore links to some classical geometric objects (such as quadratic differentials and Schwarzian derivatives), as well as some generalisations (G-opers) introduced by Beilinson and Drinfeld.