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:

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Topology of Manifolds: Interactions Between High and Low Dimensions

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Australian-German Workshop on Differential Geometry in the Large

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Aperiodic Order meets Number Theory

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Ergodic Theory, Diophantine Approximation and Related Topics

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Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases

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International Workshop on Spatial Statistics

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Mathematics of Physiological Rhythms

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Conservation Laws, Interfaces and Mixing

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Structural Graph Theory Downunder

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Tropical Geometry and Mirror Symmetry

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Early Career Researchers Workshop on Geometric Analysis and PDEs

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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.