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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.

Mathematics --- Research. --- Mathematics. --- Category theory (Mathematics). --- Homological algebra. --- Group theory. --- K-theory. --- Mathematical optimization. --- Topology. --- Category Theory, Homological Algebra. --- Group Theory and Generalizations. --- Optimization. --- K-Theory. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Algebraic topology --- Homology theory --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Homological algebra --- Algebra, Abstract --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Math --- Science --- Mathematical research --- Algebra.

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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.

Algebraic geometry. --- Dynamics. --- Ergodic theory. --- Partial differential equations. --- Category theory (Mathematics). --- Homological algebra. --- Bioinformatics. --- Computer science—Mathematics. --- Algebraic Geometry. --- Dynamical Systems and Ergodic Theory. --- Partial Differential Equations. --- Category Theory, Homological Algebra. --- Computational Biology/Bioinformatics. --- Mathematics of Computing. --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Partial differential equations --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Algebraic geometry --- Geometry --- Bio-informatics --- Biological informatics --- Biology --- Information science --- Computational biology --- Systems biology --- Homological algebra --- Algebra, Abstract --- Homology theory --- Data processing --- Mathematics. --- Geometry, Algebraic. --- Differential equations, Partial. --- Categories (Mathematics) --- Algebra, Homological.