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 Kähler–Einstein metrics and random point processes.”
Duong H. Phong on “Unification of the Kähler–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.”