Project C1: Hyper-Kähler varieties and moduli spaces

Project C1 combines algebraic cycle theory and moduli theory in the context of hyper-Kähler geometry. The two guiding goals are, on the one hand, to understand the hidden structure of the intersection theory of hyper-Kähler varieties and, on the other hand, to understand, via the theory of modular forms, the birational complexity of their moduli spaces. Key examples of such hyper-Kähler varieties arise as moduli spaces of stable objects in appropriate triangulated 2-Calabi--Yau categories.