Singular cscK Metrics on Smoothable Varieties

Explore a one-hour research seminar presented by Dr. Antonio Trusiani from Chalmers University of Technology as part of the EMG (New equivariant methods in algebraic and differential geometry) series. Delve into the extension of cscK metrics to singular varieties and discover the existence of these special metrics on Q-Gorenstein smoothable klt varieties when the Mabuchi functional is coercive. Learn about the key findings regarding the lower semicontinuity of the coercivity threshold of Mabuchi functional along degenerate families of normal compact Kähler varieties with klt singularities, and understand its implications for the openness of (uniform) K-stability in polarized families of normal projective varieties. The research presented is a collaborative effort with Chung-Ming Pan and Tat Dat Tô, offering valuable insights into advanced mathematical concepts at the intersection of algebraic and differential geometry.