MATRIX is Australia's international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-2 weeks in duration. This book is a scientific record of the 24 programs held at MATRIX in 2021-2022, including tandem workshops with Mathematisches Forschungsinstitut Oberwolfach (MFO), with Research Institute for Mathematical Sciences Kyoto University (RIMS), and with Sydney Mathematical Research Institute (SMRI).

Scientific record of research programs at MATRIX Contains articles from the 24 research programs held at MATRIX in 2021-2022 Top-level science from Australia

Autorentext
David Wood is Deputy Director of MATRIX, and Professor in the Discrete Mathematics Research Group of the School of Mathematics 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 Director of MATRIX, and Professor of Mathematics at the University of Melbourne. 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.

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Refereed Articles.- MATRIX--MFO Tandem Workshop: Invariants and Structures in Low-Dimensional Topology.- A new family of minimal ideal triangulations of cusped hyperbolic 3--manifolds.- MATRIX Program: Groups and Geometries one complex dimensional moduli spaces of hyperbolic manifolds and orbifolds: Kleinian groups and the generalised Riley slices.- MATRIX Program: Quantum Curves, Integrability and Cluster Algebras.- First properties of supermanifolds, their functor of points and the DeWitt topology.- MATRIX Program: 2D Supersymmetric Theories and Related Topics.- On Super Non-Abelian T-Duality of Symmetric and Semi-Symmetric Coset Sigma Models.- On Twisted Elliptic General Minkowski and (A)dS ground states in general 2d dilaton gravity'.- $2d$ Sigma Models and Geometry.- MATRIX Program: Structural Graph Theory Downunder II.- Product Structure of Graph Classes with Bounded Treewidth.- Notes on Aharoni's rainbow cycle conjecture.- Marc Distel, David R. Wood\newline ``Tree-Partitions with Bounded Degree Trees.- Treewidth, Circle Graphs and Circular Drawings.- MATRIX Program: Hyperbolic Differential Equations in Geometry and Physics.- Bulk-boundary correspondences and unique continuation in asymptotically Anti-de Sitter spacetimes.- Propagation of Singularities for the Wave Equation.- MATRIX Program: Mathematics of Tissue Dynamics.- Multiphase models for moving boundary problems in biology.- MATRIX Program: Mathematics of Risk 2022.- Asian Option Pricing via Laguerre Quadrature: A Diffusion Kernel Approach.- On Dupire Formula and Diffusion with Given Marginals.- Multi-Factor Polynomial Diffusion Models and Inter-Temporal Futures Dynamics.- On Autoregressive Measurement Errors in a Two-Factor Model.- On extension of the Markov chain approximation method for computing FeynmanKac type expectations.- On ruin probabilities in a Sparre Andersen type model in the presence of risky investments and random switching.- On some asymptotic expansions of skew diffusions.- Fractional Growth Portfolio Investment.- Lévy bandits under Poissonian decision times.- Entrance laws for continuous-state nonlinear branching processes coming down from infinity.- The matrix sequential probability ratio test and multivariate ruin theory.- Bayesian Parameter Estimation for Poisson AR Model.- Nonparametric {B}ayesian inference for stochastic processes with piecewise constant priors.- Quickest Changepoint Detection in General Multistream Stochastic Models: Recent Results, Applications and Future Challenges.- MATRIX Program: Mathematics of the Interactions between Brain Structure and Brain Functions.- Mathematical Foundations for Measurement of Communication Efficiency in the Human Brain.- k -Means clustering in EEG (brain waves) timeseries.- IBS-CGP & MATRIX Workshop: Symplectic Topology.- Analysis of pseudoholomorphic curves on symplectization: Revisit via contact instantons.- High-jet Relations of the Heat Kernel: Embedding Map and Applications.- Other ContributedArticles.-MATRIX-MFO Tandem Workshop: Invariants and Structures in Low-Dimensional Topology.- Pachner's Theorem.- MATRIX Program: 2D Supersymmetric Theories and Related Topics.- Vacuum Structures Revisited.- MATRIX Program: Theory and Applications of Stable Polynomials.- A large class of conjecturally stable chromatic symmetric functions.- A problem about virtual polytopes.- A conjecture on spectral sparsification with respect to hyperbolicity cones.- Topological Narayana polynomials and interlacing conjectures.