Irregular connections and Kac-Moody root systems

Understand

Some moduli spaces of irregular connections on the trivial bundle over the Riemann sphere will be identified with Nakajima quiver varieties.

• In particular this enables us to associate a Kac-Moody root system to such connections (yielding many isomorphisms between such moduli spaces, via the reflection functors for the corresponding Weyl group).
• The possibility of 'reading' a quiver in different ways also yields numerous isomorphisms between such moduli spaces, often between spaces of connections on different rank bundles and with different polar divisors.
• Finally some results of Crawley-Boevey on the existence of stable connections will be extended to this more general context.