Differential geometry, Calabi-Yau theory, and general relativity

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 KhlerEinstein metrics and random point processes. Duong H. Phong on Unification of the KhlerRicci 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 CalabiYau manifolds.