2016 MATRIX Annals (eBook)

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 (Chapters 1-5 and 18-21); 
• Winter of Disconnectedness (Chapter 6 and 22-26); 
• Approximation and Optimisation (Chapters 7-8);
• Refining C*-Algebraic Invariants for Dynamics using KK-theory (Chapters 9-13);
• Interactions between Topological Recursion, Modularity, Quantum Invariants and Low-dimensional Topology (Chapters 14-17 and 27).
  

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.

David R. 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 E. Praeger AM FAA is Professor of Mathematics at the University of Western Australia. She is the Foreign Secretary of the Australian Academy of Science, a former ARC Federation Fellow, and inaugural Director of the UWA Centre for the Mathematics of Symmetry and Computation. Cheryl's research has focussed 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 cot of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics.