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Publisher’s description: 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:

\(\bullet\)

Higher Structures in Geometry and Physics (Chapters 1–5 and 18–21);

\(\bullet\)

Winter of Disconnectedness (Chapter 6 and 22–26);

\(\bullet\)

Approximation and Optimisation (Chapters 7–8);

\(\bullet\)

Refining C\(^*\)-Algebraic Invariants for Dynamics using KK-theory (Chapters 9–13);

\(\bullet\)

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.
The articles of this volume will be reviewed individually.
Indexed articles:
Rogers, Christopher L., Homotopical properties of the simplicial Maurer-Cartan functor, 3-15 [Zbl 1448.18035]
Barwick, Clark; Shah, Jay, Fibrations in \(\infty\)-category theory, 17-42 [Zbl 1448.18031]
Roberts, David Michael; Vozzo, Raymond F., The smooth Hom-stack of an orbifold, 43-47 [Zbl 1404.58031]
Riehl, Emily, Complicial sets, an overture, 49-76 [Zbl 1409.18018]
Drummond-Cole, Gabriel C., A non-crossing word cooperad for free homotopy probability theory, 77-99 [Zbl 1439.46053]
Glöckner, Helge, Endomorphisms of Lie groups over local fields, 101-165 [Zbl 1412.22011]
Roshchina, Vera; Sang, Tian; Yost, David, Compact convex sets with prescribed facial dimensions, 167-175 [Zbl 1403.52005]
Sukhorukova, Nadezda; Ugon, Julien; Yost, David, Chebyshev multivariate polynomial approximation: alternance interpretation, 177-182 [Zbl 1401.41019]
Goffeng, Magnus; Mesland, Bram, Spectral triples on \(O_N\), 183-201 [Zbl 1448.19005]
Bourne, Chris; Schulz-Baldes, Hermann, Application of semifinite index theory to weak topological phases, 203-227 [Zbl 1442.19016]
Eilers, Søren; Restorff, Gunnar; Ruiz, Efren; Sørensen, Adam P. W., Filtered \(K\)-theory for graph algebras, 229-249 [Zbl 1448.19007]
Arici, Francesca, Gysin exact sequences for quantum weighted Lens spaces, 251-262 [Zbl 1409.58002]
Deeley, Robin J., A signed version of Putnam’s homology theory: Lefschetz and zeta functions, 263-276 [Zbl 1401.37030]
Kashaev, Rinat, A simple model of 4d-TQFT, 277-286 [Zbl 1402.81235]
Licata, Joan E.; Mathews, Daniel V., Morse structures on partial open books with extendable monodromy, 287-303 [Zbl 1407.53087]
Shabat, George, Counting Belyi pairs over finite fields, 305-322 [Zbl 1426.14008]
Spreer, Jonathan; Tillmann, Stephan, Unravelling the dodecahedral spaces, 323-347 [Zbl 1409.57020]
Hackney, Philip; Robertson, Marcy, Lecture notes on infinity-properads, 351-374 [Zbl 1448.18028]
Kaufmann, Ralph M., Lectures on Feynman categories, 375-438 [Zbl 1448.18019]
Yalin, Sinan, Moduli spaces of (bi)algebra structures in topology and geometry, 439-488 [Zbl 1403.14040]
Turchin, Victor, Embedding calculus and the little discs operads, 489-500 [Zbl 1403.57024]
Le Boudec, Adrien, Groups of automorphisms and almost automorphisms of trees: subgroups and dynamics, 501-523 [Zbl 1442.20014]
Reid, Colin D., Normal subgroup structure of totally disconnected locally compact groups, 525-560 [Zbl 1402.22004]
Thomas, Anne, Automorphism groups of combinatorial structures, 561-592 [Zbl 1404.22052]
Wesolek, Phillip, A survey of elementary totally disconnected locally compact groups, 593-611 [Zbl 1402.22005]
Willis, George, The scale, tidy subgroups and flat groups, 613-636 [Zbl 1403.22005]
van der Veen, Roland, Introduction to quantum invariants of knots, 637-656 [Zbl 1403.57011]