In 2019, mathematicians around the world celebrated the 70th birthday of Professor Shing-Tung Yau and expressed their appreciation and admiration. A number of conferences were held throughout the year for this special occasion: 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 (November), and elsewhere.

This is the second of the two Surveys in Differential Geometry volumes in honor of Professor Yau, consisting of articles by some of the speakers at those special conferences, and several additional contributions.

The articles in this volume include: Tristan C. Collins and Yun Shi, "Stability and the deformed Hermitian Yang–Mills equation"; Simon Donaldson and Christopher Scaduto, "Associative submanifolds and gradient cycles"; Davide Gaiotto and Edward Witten, "Probing quantization via branes"; L. Gottsche and M. Kool, "Sheaves on surfaces and virtual invariants"; Goo Ishikawa and Stanislaw Janeczko, "Symplectic singularities of differentiable mappings"; Jun Li and Chiu-Chu Melissa Liu, "Counting curves in quintic Calabi–Yau threefolds and Landau-Ginzberg models"; Nikolai Nadirashvili et al., "Conformally maximal metrics for Laplace eigenvalues on surfaces"; Kieran G. O'Grady, "Moduli of sheaves on $K3$'s and higher dimensional HK varieties"; Richard Schoen and Shing-Tung Yau "Positive scalar curvature and minimal hypersurface singularities"; Penny Smith and Karen Uhlenbeck, "Removeability of a codimension four singular set for solutions of a Yang–Mills–Higgs equation with small energy"; and Mu–Tao Wang, "Limits of quasi-local angular momentum on an isolated gravitating system".