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.