Lectures given at the 2021 Tsinghua conference celebrating the 110th birthday of S.-S. Chern. This special volume is dedicated to S.-S. Chern in honor of his 110th birthday. It is based on talks given at the conference ""Chern: a Great Geometer of the 20th Century"" held at Tsinghua University in Beijing, China, October 10-14, 2021.