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.