Speaker: Michael Barz (Princeton University)

Title: Irregular connections and the Stokes phenomena

Abstract: 

Deligne's book focuses mostly on connections with regular singularities -- in the 1970s, Deligne found connections with irregular singularities to be pathological (see his article "Pourquoi un géomètre algébriste s'intéresse-t-il aux connexions irrégulières?"). But since then, Deligne, Malgrange, Sibuya, and many others have noticed that irregular connections are home to many interesting phenomena which seem to mirror things occurring for ell-adic sheaves.

Regular connections are the simplest to understand since, by Riemann-Hilbert, they are completely determined by the monodromy of their solutions. Unfortunately, this fails for irregular connections -- there are nontrivial irregular connections whose solutions have no monodromy. In this talk we describe the Stokes data which one can use to help understand irregular connections.

Reference: Malgrange, Équations Différentielles à Coefficients Polynomiaux, chapters 3 and 4