© 2020

2018 MATRIX Annals

  • David R. Wood (Editor-in-Chief)
  • Jan de Gier
  • Cheryl E. Praeger
  • Terence Tao

Part of the MATRIX Book Series book series (MXBS, volume 3)

Table of contents

  1. Front Matter
    Pages i-xxxii
  2. Refereed Articles On the Frontiers of High Dimensional Computation

    1. Front Matter
      Pages 3-4
    2. J. C. H. Blake, I. G. Graham, F. Scheben, A. Spence
      Pages 5-15
    3. Mahadevan Ganesh, Stuart C. Hawkins
      Pages 17-27
    4. Alexander D. Gilbert, Ivan G. Graham, Robert Scheichl, Ian H. Sloan
      Pages 29-43
    5. Fred J. Hickernell, Peter Kritzer, Henryk Woźniakowski
      Pages 61-78
    6. Yoshihito Kazashi, Ian H. Sloan
      Pages 79-96
    7. Hrushikesh N. Mhaskar, Sergei V. Pereverzyev, Vasyl Yu. Semenov, Evgeniya V. Semenova
      Pages 113-119
  3. Refereed Articles Month of Mathematical Biology

    1. Front Matter
      Pages 135-135
    2. Ana Victoria Ponce Bobadilla, Bartosz Jan Bartmanski, Ramon Grima, Hans G. Othmer
      Pages 137-147
    3. Stuart T. Johnston, Christopher N. Angstmann, Satya N.V. Arjunan, Casper H.L. Beentjes, Adrien Coulier, Samuel A. Isaacson et al.
      Pages 149-164
  4. Refereed Articles Recent Trends on Nonlinear PDEs of Elliptic And Parabolic

    1. Front Matter
      Pages 165-165
    2. Elisa Affili, Serena Dipierro, Enrico Valdinoci
      Pages 167-182
    3. Serena Dipierro, Pietro Miraglio, Enrico Valdinoci
      Pages 229-248
    4. François Hamel, Nikolai Nadirashvili, Yannick Sire
      Pages 249-263

About this book


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

Editors and affiliations

  • David R. Wood (Editor-in-Chief)
    • 1
  • Jan de Gier
    • 2
  • Cheryl E. Praeger
    • 3
  • Terence Tao
    • 4
  1. 1.School of MathematicsMonash UniversityMelbourneAustralia
  2. 2.School of Mathematics and StatisticsUniversity of MelbourneParkvilleAustralia
  3. 3.Department of Mathematics and StatisticsThe University of Western AustraliaPerthAustralia
  4. 4.Department of MathematicsUniversity of California Los AngelesLos AngelesUSA

About the editors

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.

Bibliographic information