Lax Pairs and Spectral Curves for Calogero–Moser and Spin Calogero–Moser Systems

We summarize recent results on the construction of Lax pairs with spectral parameter for the twisted and untwisted elliptic Calogero–Moser systems associated with arbitrary simple Lie algebras, their scaling limits to Toda systems, and their role in Seiberg–Witten theory. We extend part of this work by presenting a new parametrization for the spectral curves for elliptic spin Calogero–Moser systems associated with $SL(N)$.