Abstract
The classification of 5d SCFTs has a strong resemblance to a mathematical classification problem: we want to list classes of  (physical) objects, and to elucidate the relations (morphisms) among them. Indeed, this is more than a coincidence, as M-theory naturally rephrases the problem in terms of the classification of canonical threefold singularities (CY3s). 
 
In this talk, I will present a recent attempt at this classification, together with a novel presentation of such SCFTs/CY3s, based on generalized quivers. I will highlight the physics and the geometry of such objects, the relations (dualities) among them, and how our program led us to the discovery of  "exotics": SCFTs/CY3s whose existence sheds light on the whole class that we are studying.
 
Based on
2311.04984 [MDM, M. Del Zotto, M. Graffeo, A. Sangiovanni],
2502.04431 [MDM, M. Del Zotto, J. Grimminger, A. Sangiovanni],
25xx.xxxxx [MDM, M. Del Zotto, M. Graffeo, A. Sangiovanni]
25xx.xxxxx [A. Bourget, MDM, M. Del Zotto, J. Grimminger, A. Sangiovanni]