2018 MATRIX Annals

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.

• Mathematical Research Institute MATRIX
• special functions
• algebraic geometry
• approximation
• optimisation
• high dimensional computation
• mathematical biology
• dynamics
• low dimensional geometry
• nonlinear PDEs
• representation theory
• partial differential equations

• School of Mathematics, Monash University, Melbourne, Australia

  David R. Wood

• School of Mathematics and Statistics, University of Melbourne, Parkville, Australia

  Jan de Gier

• Department of Mathematics and Statistics, The University of Western Australia, Perth, Australia

  Cheryl E. Praeger

• Department of Mathematics, University of California Los Angeles, Los Angeles, USA

  Terence Tao

David Wood is co-Director of MATRIX, and Professor in the Discrete Mathematics Research Group of the School of Mathematical Sciences at Monash University. David’s research interests are in discrete mathematics and theoretical computer science, especially structural graph theory, extremal graph theory, geometric graph theory, graph colouring, and combinatorial geometry.

Jan de Gier is co-Director of MATRIX, and Professor and Head of the School of Mathematics and Statistics at the University of Melbourne. He is also Chief Investigator of the ARC Centre of Excellence for Mathematical and Statistical Frontiers. Jan’s main research areas are mathematical physics, statistical mechanics, interacting particle systems, solvable lattice models, representation theory and multivariable polynomials. He also studies applications of stochastic particle systems to real world traffic modelling.

Cheryl Praeger AM FAA is Emeritus Professor of Mathematics at the University of Western Australia. She is former Foreign Secretary of the Australian Academy of Science, former Member-at-Large of the Executive of the International Mathematical Union, former ARC Federation Fellow, and was the inaugural Director of the UWA Centre for the Mathematics of Symmetry and Computation. Cheryl’s research has focused on the theory of group actions and their applications in algebraic graph theory and for combinatorial designs; and algorithms for group computation including questions in statistical group theory and algorithmic complexity.

Terence Tao FAA FRS is an Australian-American mathematician who works in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing and analytic number theory. He holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles. Tao was a co-recipient of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics.

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