Title:Â On Fano and Calabi-Yau pairs of small coregularity.Abstract:Â The coregularity is an invariant that measures a specific type of combinatorial complexity of a pair. We will start this talk by defining this invariant and giving some examples. Then, we will explain how results about complements of Fano varieties of bounded dimension are still valid for Fano […]
Title:Â Minimal model program for algebraically integrable foliations and generalized pairs.Abstract:Â In this talk, I will discuss my recent research that establishes the minimal model program for Q-factorial foliated dlt algebraically integrable foliations and log canonical generalized pairs. This is joint work with G. Chen, J. Han, and L. Xie.
Title:Â A non-Archimedean characterization of local K-stability.Abstract:Â Log Fano cone singularities are generalizations of affine cones over Fano varieties. Motivated by the study of canonical metrics on Fano varieties, there is a local K-stability theory characterizing the existence of Ricci-flat K"ahler cone metrics on log Fano cone singularities. In this talk, we aim to give a non-Archimedean […]