The de Rham stack in analytic geometry

The de Rham stack in algebraic geometry is a geometric object that encodes the theory of D-modules in its theory of quasi-coherent sheaves. Motivated from this, using the approach of Clausen-Scholze of analytic geometry, one can construct different incarnations of the Rham stack that encode different theories of analytic D-modules. In this talk I shall explain some of the ideas behind these constructions and their relation with more classical theories of differential equations.