Super-Global Program at Waseda University

Title: An introduction to Opers.

Abstract: 

 An Oper is a holomorphic connection on a vector bundle which induces a filtration on it. This connection satisfies some special properties which allow for the construction of a differential operator between two line bundles, related to the filtration.

 Opers were first introduced by Drinfeld-Sokolov in 1984 in relation to certain differential equations. This notion was then adapted to a Riemann surface by Beilinson-Drinfeld for applications in the geometric Langlands program. More recently, several authors have studied the link between opers and certain connected components , called Hitchin components, parameterizing certain representations of the fundamental group of the Riemann surface. 

 The goal of this talk is to introduce the notion of Oper, build the differential operator associated to it and to give an example on the Riemann sphere.