This is the first of two volumes consisting of lectures given at conferences held in 2019 to celebrate the seventieth birthday of Shing-Tung Yau: at Harvard University (May), at the University of Rome (May/June), at the Chinese University of Hong Kong (June), at the 8th ICCM Congress at Tsinghua University (June), at Lehigh University in Pennsylvania (November), and elsewhere.

Included here are:

Werner Ballmann on "Bottom of spectra and coverings."
Robert J. Berman with "An invitation to Kahler-Einstein metrics and random point processes."
Duong H. Phong on "Unification of the Kahler-Ricci and anomaly flows"
Cumrun Vafa on "SCFTs, holography, and topological strings"
Stephen S.-T. Yau on "Recent results on kk-th Yau algebras over simple elliptic singularities E~6E~6"
Kefeng Liu on "Global methods of solving equations on manifolds"
Chuu-Lian Terng on "The geometric airy curve flow on RnRn"
Valentino Tosatti on "Collapsing Calabi-Yau manifolds."