Title: On the irreducible case of Fargues' conjecture for GL_n

Abstract: In 2014, Fargues formulated a striking conjecture, which very 
roughly says that geometric Langlands works over the Fargues-Fontaine 
curve and provides a geometrization of the classical local Langlands 
correspondence. I will first recall what the main geometric players are 
and what the conjecture says (with special emphasis on the case of 
GL_n), and will then discuss joint work with Johannes Anschütz, 
regarding the case where the group is GL_n and where one starts with an 
irreducible Weil-Deligne representation in the conjecture.