The Rescaling Method on Subvarieties of Bounded Symmetric Domains

Explore the rescaling method on subvarieties of bounded symmetric domains in this lecture by Ngaiming Mok at ICBS2024. Delve into Eugenio Calabi's seminal work on the diastasis and extension theorems for holomorphic isometries. Examine the algebraicity theorem for germs of holomorphic isometries between bounded symmetric domains. Discover how the study of holomorphic isometries led to the Ax-Lindemann-Weierstrass Theorem for quotients of complex unit balls by arbitrary lattices. Investigate the asymptotic behavior of holomorphic isometries of the Poincaré disk and its connection to a uniformization theorem for projective varieties. Learn how these concepts contribute to proving the Ax-Lindemann-Weierstrass theorem for quotients of bounded symmetric domains by arbitrary cocompact lattices.