Origins of geometric Langlands

I will tell (part of) the origin story of geometric Langlands. Motivated by zeta functions, we will discuss algebraic geometry over finite fields and the “sheaf-function dictionary” following Weil, Grothendieck, and Deligne. We will introduce geometric Langlands as part of this philosophy. Finally, we will survey some recent developments extending these older ideas. The goal of the talk is to give a big picture perspective without getting bogged down in technicalities.