MATRIX is Australia's international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the ten programs held at MATRIX in 2019 and the two programs held in January 2020: - Topology of Manifolds: Interactions Between High and Low Dimensions- Australian-German Workshop on Differential Geometry in the Large- Aperiodic Order meets Number Theory- Ergodic Theory, Diophantine Approximation and Related Topics- Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases- International Workshop on Spatial Statistics- Mathematics of Physiological Rhythms- Conservation Laws, Interfaces and Mixing- Structural Graph Theory Downunder- Tropical Geometry and Mirror Symmetry- Early Career Researchers Workshop on Geometric Analysis and PDEs- Harmonic Analysis and Dispersive PDEs: Problems and ProgressThe articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.