​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 eight programs held at MATRIX in its second year, 2017:- Hypergeometric Motives and Calabi–Yau Differential Equations- Computational Inverse Problems- Integrability in Low-Dimensional Quantum Systems- Elliptic Partial Differential Equations of Second Order: Celebrating 40 Years of Gilbarg and Trudinger’s Book- Combinatorics, Statistical Mechanics, and Conformal Field Theory- Mathematics of Risk- Tutte Centenary Retreat- Geometric R-Matrices: from Geometry to ProbabilityThe 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.