The Lax project

For each classical integrable system there is often a "Lax pair", which is basically a meromorphic Higgs bundle on the trivial bundle on the Riemann sphere. Thus we can consider the corresponding wild Hitchin moduli space which is a complete hyperkahler manifold. Thus we have a map from integrable systems to complete hyperkahler manifolds.

The project is to go though the integrable systems literature and compile a list Lax pairs and the corresponding irregular curve and the resulting hyperkahler manifold. Further in the cases where integrable systems have alternative Lax pairs, show that the corresponding hyperkahler manifolds are isomorphic.