Abstract

The Deligne-Simpson problem asks for the existence of meromorphic G-connections withprescribed local behavior at the poles. l will explain joint work with Zhiwei Yun in which we give asolution to this problem for G-connections on P^1 with two poles, one of which is regular singularwith residue in a fixed nilpotent orbit, the other of which is irregular and satisfies a condition that wecall isoclinic (all slopes are equal). Perhaps surprisingly, our solution is related to the representationtheory of the rational Cherednik algebra. lf time permits, l will discuss ioint work with Andreas Hohlregarding unigueness (rigidity) of the solution for two famous families of such G-connections, theKloosterman (aka Frenkel-Gross) G-connection and the Airy G-connection. Our approach is basedon the Stokes phenomenon for irregular connections.