Sabbah-Mochizuki-Kedlaya’s Hukuhara-Levelt-Turrittin Theorem

When I first started learning about irregular perverse sheaves, I struggled to find a clear answer to the question: “what does an irregular perverse sheaf look like, in the simplest cases? What should be my intuition?” If I don’t know about the motivation from differential equations, how can I picture them? This is not yet

Deligne’s regular solution in dimension 1

In this post, I want to recall the elements of the regular Riemann-Hilbert Correspondence (but only in dimension 1, on our small disk around the origin). We’ll talk more about the category of Meromorphic Connections on with singularities at 0, and how they’re just a different way of phrasing linear ODEs whose solutions have singularities