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 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.