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 K?hler-Einstein metrics and random point processes." Duong H. Phong on "Unification of the K?hler-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."
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