Investigating the boundedness of the Calabi-Yau algebraic varieties
Calabi-Yau manifolds are one of the most important building blocks of algebraic varieties. Advancing understanding of the geometry and the classification of Calabi-Yau varieties would yield applications in theoretical physics as they satisfy the requirement of space for the six ‘unseen’ spatial dimensions of string theory. Investigating whether there are many families of Calabi-Yau varieties in any fixed dimension – a property called boundedness – remains a long-standing challenge. Funded by the Marie Skłodowska-Curie Actions programme, the BoundModProbAG project aims to prove that there is essentially a finite number of families of Calabi-Yau varieties with some extra piece of structure – an elliptic fibration – in any dimension.