Abstract: Local K-stability is the algebro-geometric criterion for the existence of a Ricci-flat Kähler cone metric on a log Fano cone singularity, which itself is a generalization of affine cones over Fano varieties. By a result of Li-Xu, to test K-stability of Fano varieties, it suffices to test the so-called ‘special’ test configurations. In this talk, we will talk about a local version of this result for log Fano cone singularities. Our method relies on a non-Archimedean characterization of local K-stability. This is joint work with Yuchen Liu.

Biography: Yueqiao Wu is currently a J.J. Sylvester Assistant Professor at Johns Hopkins University. She finished her PhD at the University of Michigan in 2023, advised by Mattias Jonsson. She is interested in applications of non-Archimedean techniques in algebraic geometry and complex geometry.

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