Explicit K-moduli spaces-- Yuchen Liu, December 18, 2020

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K-stability has become a central tool in contructing moduli spaces for Fano varieties, called K-moduli spaces. In this talk I will discuss the recent progress on explicit construction of these moduli spaces, mainly focusing on cubic threefolds and fourfolds whose K-moduli spaces coincide with GIT. An essential ingredient is the use of normalized volumes to control singularities at the boundary of K-moduli spaces. This talk is partly based on joint work with Chenyang Xu.