Higher-dimensional log Calabi-Yau pairs

Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that measure their combinatorial complexity, explore how additional structures (like the existence of a symplectic form) constrain their geometry, and ultimately recognize that only finitely many geometries of the types above can actually occur.

The main topics for the workshop will be:

1) The birational complexity of log Calabi-Yau pairs and its connection to rationality of smooth Fano varieties and cluster geometry.

2) Mukai’s conjecture for Fano varieties and its relation to the generalized complexity.

3) Geometry and deformation of symplectic log Calabi–Yau pairs and its relation to compact hyperkähler and character varieties.

4) Boundedness problems for Calabi–Yau varieties and its connection with moduli theory, e.g., for elliptic Calabi–Yau 3-folds.