Homological Classification of 4d $\mathcal{N}=2$ QFT. Part I: Rank-1 revisited

Understand

Argyres and co-workers started a program to classify all 4d $\mathcal{N}=2$ QFT by classifying Special Geometries with appropriate properties.

• They completed the program in rank-1.
• Rank-1 $\mathcal{N}=2$ QFT are equivalently classified by the Mordell-Weil groups of certain rational elliptic surfaces.
• The classification of 4d $\mathcal{N}=2$ QFT is also conjectured to be equivalent to the representation theoretic (RT) classification of all 2-Calabi-Yau categories with suitable properties.