MATRIX is Australia’s international, residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each lasting 1-4 weeks. This book is a scientific record of the five programs held at MATRIX in its first year, 2016: - Higher Structures in Geometry and Physics - Winter of Disconnectedness - Approximation and Optimisation - Refining C*-Algebraic Invariants for Dynamics using KK-theory - Interactions between Topological Recursion, Modularity, Quantum Invariants and Low- dimensional Topology The MATRIX Scientific Committee selected these programs based on their scientific excellence and the participation rate of high-profile international participants. Each program included ample unstructured time to encourage collaborative research; some of the longer programs also included an embedded conference or lecture series. The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on selected topics related to the MATRIX program; the remaining contributions are predominantly lecture notes based on talks or activities at MATRIX.

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 2018: - Non-Equilibrium Systems and Special Functions - Algebraic Geometry, Approximation and Optimisation - On the Frontiers of High Dimensional Computation - Month of Mathematical Biology - Dynamics, Foliations, and Geometry In Dimension 3 - Recent Trends on Nonlinear PDEs of Elliptic and Parabolic Type - Functional Data Analysis and Beyond - Geometric and Categorical Representation Theory 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.

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.

​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 Probability 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.

MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-2 weeks in duration. This book is a scientific record of the 24 programs held at MATRIX in 2021-2022, including tandem workshops with Mathematisches Forschungsinstitut Oberwolfach (MFO), with Research Institute for Mathematical Sciences Kyoto University (RIMS), and with Sydney Mathematical Research Institute (SMRI).

This book presents covariance matrix estimation and related aspects of random matrix theory. It focuses on the sample covariance matrix estimator and provides a holistic description of its properties under two asymptotic regimes: the traditional one, and the high-dimensional regime that better fits the big data context. It draws attention to the deficiencies of standard statistical tools when used in the high-dimensional setting, and introduces the basic concepts and major results related to spectral statistics and random matrix theory under high-dimensional asymptotics in an understandable and reader-friendly way. The aim of this book is to inspire applied statisticians, econometricians, and machine learning practitioners who analyze high-dimensional data to apply the recent developments in their work.

This book tackles issues associated with inconsistency in pairwise comparisons from both theoretical and practical perspectives. Human judgments are seldom absolutely consistent, or absolutely precise, therefore problems of measuring and handling inconsistency belong among hot topics of the current research, especially in the theoretical framework of multiple criteria decision aiding (MCDA). The book presents and discusses the state-of-the-art of this field including both cardinal and ordinal inconsistency, the problems of different scales for comparisons and inconsistency reduction, and the alternative approaches to inconsistency detection and measurement. This book is a unique one-stop guide for readers who are interested in inconsistency in pairwise comparisons. Researchers and practitioners in the area of multiple-criteria decision-making (MCDM) and the analytic hierarchy process (AHP) will find this informative book particularly valuable.