# 2016 MATRIX Annals

The 2016 MATRIX Annals, the first book in the MATRIX Book Series, documents scientific activities at MATRIX in its first year. Please find below pre-publication versions of the articles in the book.

## Refereed Articles

### Higher Structures in Geometry and Physics

Christopher L. Rogers.

Homotopical properties of the simplicial Maurer-Cartan functor.

Clark Barwick, Jay Shah.

Fibrations in ∞-category theory.

David Michael Roberts, Raymond F. Vozzo.

The smooth Hom-stack of an orbifold.

Emily Riehl.

Complicial sets, an overture.

Gabriel C. Drummond-Cole.

A non-crossing word cooperad for free homotopy probability theory.

### Winter of Disconnectedness

Helge Glöckner.

Endomorphisms of Lie groups over local fields.

### Approximation and Optimisation

Vera Roshchina, Tian Sang, David Yost.

Compact convex sets with prescribed facial dimensions.

Nadezda Sukhorukova, Julien Ugon, David Yost.

Chebyshev multivariate polynomial approximation: alternance interpretation.

### Refining C* Algebraic Invariants for Dynamics using KK-Theory

Magnus Goffeng, Bram Mesland.

Spectral triples on O_{N}.

Chris Bourne, Hermann Schulz-Baldes.

Application of semifinite index theory to weak topological phases.

Søren Eilers, Gunnar Restorff, Efren Ruiz, Adam P. W. Sørensen.

Filtered K-theory for graph algebras.

Francesca Arici.

Gysin exact sequences for quantum weighted lens spaces.

Robin J Deeley.

A signed version of Putnam’s homology theory: Lefschetz and zeta functions.

### Interactions between Topological Recursion, Modularity, Quantum Invariants and Low-dimensional Topology

Rinat Kashaev.

A simple model of 4d-TQFT.

Joan E. Licata, Daniel V. Mathews.

Morse structures on partial open books with extendable monodromy.

George Shabat.

Counting Belyi maps over finite fields.

Jonathan Spreer, Stephan Tillmann.

Unravelling the dodecahedral spaces.

## Other Contributed Articles

### Higher Structures in Geometry and Physics

Philip Hackney, Marcy Robertson.

Lecture notes on infinity-properads.

Ralph Kaufmann.

Lectures on Feynman categories.

Sinan Yalin.

Moduli spaces of (bi)algebra structures in topology and geometry.

Victor Turchin.

Embedding calculus and the little discs operads.

### Winter of Disconnectedness

Adrien Le Boudec.

Groups of automorphisms and almost automorphisms of trees: subgroups and dynamics.

Colin D. Reid.

Normal subgroup structure of totally disconnected locally compact groups.

Anne Thomas.

Automorphism groups of combinatorial structures.

Phillip Wesolek.

A survey of elementary totally disconnected locally compact groups.

George Willis.

The scale, tidy subgroups and flat groups.

### Interactions between Topological Recursion, Modularity, Quantum Invariants and Low-dimensional Topology

Roland van der Veen.

Introduction to quantum invariants of knots.