Notions of K-stability attracted interest as purely algebro-geometric characterisations of the existence of Kähler-Einstein metrics on Fano manifolds. Since then, exciting developments in the field have shown that shows that K-stability is also the right framework to understand the moduli theory of Fano varieties – or in layman’s terms, how Fano varieties behave in families. Yet, our understanding of K-stability is still very partial!

Birational geometry gives us tools to further this understanding and to construct geometrically meaningful degenerations of Fano manifolds. This interplay between birational geometry, moduli theory and K-stability was at the heart of the workshop.