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.