In 2021, Australia’s residential research institute for the mathematical sciences MATRIX welcomed The University of Queensland as Associate Member alongside ACEMS, supporting its partners the Australian National University, Monash University and The University of Melbourne.

In exciting news, and in recognition of its role as critical infrastructure for mathematical science research collaboration in Australia and the Asia-Pacific, MATRIX was awarded unprecedented funding from the Australian Research Council (ARC) through its Linkage Infrastructure, Equipment and Facilities (LIEF) program.

MATRIX has enhanced its international reach by partnering with the German Mathematisches Forchungsinstitut Oberworlfach (MFO) in 2021 to host two online research tandem workshops. Each workshop took place simultaneously in parallel at both institutes, interacting via a common online conference platform enabled by high resolution audio-visual technology; a first for both institutes.

MATRIX continued to host an international online seminar series featuring very high profile national and international speakers.

On the domestic front, starting in December 2020, MATRIX and the Australian Mathematical Sciences Institute (AMSI) have supported Australian-based PhD students throughout the pandemic by hosting highly successful online PhD student-led research symposia, which have attracted a diverse range of domestic and international academic participants at all career stages, as well as external participants from business, industry and government.

Together with the Sydney Mathematical Research Institute (SMRI), MATRIX also hosted four online research programs, including an online multi-week symposium featuring Fields Medallist Martin Hairer.

Due to the impact of COVID-19, MATRIX was limited to hosting four excellentresearch programs in-person at Creswick during 2021:

• Integrability and Combinatorics at Finite Temperature
• Isoperimetric Inequalities in Geometric Partial Differential Equations
• Women in Geometry, Analysis and Topology
• Quantum Curves, Integrability and Cluster Algebras.

MATRIX continued its Outreach Program and co-hosted MathsCraft with ACEMS, for school students from Grades 5 through to Year 10, with mathematicians and students working on interesting and challenging maths problems.

In 2021, MATRIX released the fourth edition in its book series, 2019-2020 MATRIX Annals, published by Springer. This book is a scientific record of the ten research programs held at MATRIX in 2019 and 2020. The MATRIX Book Series has been encyclopaedic with 656 pages in 2016, 691 pages in 2017, 427 pages in 2018 and 803 pages in 2019-20 for a total of 2577 pages in five years (2020 inclusive). A fifth edition, 2021-2022 MATRIX Annals, will be published in early 2023.

MATRIX looks forward to a busy 2022, with 13 research programs planned:

• MATRIX-SMRI Symposium: Singularities in Geometric Flows – An Ancient Perspective
• MATRIX-SMRI Symposium: Nijenhuis geometry and integrable systems
• 2D Supersymmetric Theories and Related Topics
• Dynamics, Foliations, and Geometry II
• Frontiers in Representation Theory
• Hyperbolic Differential Equations in Geometry and Physics
• Theory and Applications of Stable Polynomials
• Structural Graph Theory Downunder II
• Spectrum and Symmetry for Group Actions in Differential Geometry
• Mathematics of Tissue Dynamics
• Cell Motility in Dynamic Environments
• Complex Networks Winter Workshop
• IBS-CGP and MATRIX workshop on Symplectic Typology.

Further information: https://www.matrix-inst.org.au/

MATRIX is deeply grateful for the support from the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), without which it would not be able to support the mathematical sciences in Australia at the level that it does today.

Some participants at the “Women in Geometry, Analysis and Topology” research program held in-person at Creswick, 15-19 November 2021.