Uniformization, Calogero-Moser/Heun duality and Sutherland/bubbling pants

Understand

Inspired by the work of Alday, Gaiotto and Tachikawa (AGT), we saw the revival of Poincar{\'{e}}'s uniformization problem and Fuchsian equations obtained thereof.

• Three distinguished aspects are possessed by Fuchsian equations.
• First, they are available via imposing a classical Liouville limit on level-two null-vector conditions.
• Second, they fall into some A_1-type integrable systems.