Title:

Moduli spaces of higher dimensional varieties

Abstract:

One feature of Algebraic Geometry is  that the parameterising space of a natural class of objects often itself forms an algebraic geometry object, but this usually can be seen only after a hard work! The moduli spaces of curves are probably the most studied objects in algebraic geometry. In this talk, I will discuss higher dimensional analogues. More precisely, I will  talk about the construction of compact Hausdorff moduli spaces parameterising higher dimensional varieties, in both the negatively curved case called (KSBA) and the positive curved case (called Fano).