Calla Tschanz (Bochum): From logarithmic Hilbert schemes to degenerations of hyperkähler varieties

In this talk, I will discuss my previous work on constructing explicit models of logarithmic Hilbert schemes. This relates to work or Li-Wu on expanded degenerations, Gulbrandsen-Halle-Hulek on degenerations of Hilbert schemes of points and Maulik-Ranganathan on logarithmic Hilbert schemes. The constructions I consider are local. I will then explain how we globalise these in joint work with Shafi and apply them to construct minimal type III degenerations of hyperkähler varieties, namely Hilbert schemes of points on K3 surfaces.