"Moduli and Stability conditions"
July 29th--August 2nd, 2019
Leibniz Universität Hannover
Arend Bayer: "Stability conditions in families".
I will give an introduction to stability conditions on derived categories, followed by a survey of their applications in algebraic geometry. I will then focus on the recent construction of stability conditions in families, along with geometric examples and applications.
Sándor Kovács: "Singularities and moduli theory of KSB stable varieties"
In these series of lectures I will discuss the construction of compact moduli spaces of canonically polarized varieties of arbitrary dimension. Special attention will be paid to the similarities and differences compared to the theory of moduli of curves. In particular, I will discuss the relevant classes of singularities, their connections with one another, and some of their most important properties. Time permitting I will also mention recent results regarding these moduli spaces.
Chenyang Xu: "K-stability, Fano and moduli".
This lecture series will discuss the recent progress on K-stability of Fano varieties, with the focus on using it to construct a ’nice' moduli space. This is an outcome of a deep interplay between higher dimensional geometry (e.g. MMP) and ideas originated in the Kähler-Einstein problem. We will start from the basic definition of K-stability, and then discuss the valuative criterion in both local and global setting. Finally, we will apply them to the study of K-moduli problem.
Foundation Compositio Mathematica