MATRIX is Australia 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 Progress The 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.