2016 Matrix Annals 1st Ed. 2018

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 - Winter of Disconnectedness - Approximation and Optimisation - Refining C*-Algebraic Invariants for Dynamics using KK-theory - Interactions between Topological Recursion, Modularity, Quantum Invariants and Low- dimensional Topology 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. Front Matter ....Pages i-xxix Front Matter ....Pages 1-1 Homotopical Properties of the Simplicial Maurer–Cartan Functor (Christopher L. Rogers)....Pages 3-15 Fibrations in ∞-Category Theory (Clark Barwick, Jay Shah)....Pages 17-42 The Smooth Hom-Stack of an Orbifold (David Michael Roberts, Raymond F. Vozzo)....Pages 43-47 Complicial Sets, an Overture (Emily Riehl)....Pages 49-76 A Non-crossing Word Cooperad for Free Homotopy Probability Theory (Gabriel C. Drummond-Cole)....Pages 77-99 Endomorphisms of Lie Groups over Local Fields (Helge Glöckner)....Pages 101-165 Compact Convex Sets with Prescribed Facial Dimensions (Vera Roshchina, Tian Sang, David Yost)....Pages 167-175 Chebyshev Multivariate Polynomial Approximation: Alternance Interpretation (Nadezda Sukhorukova, Julien Ugon, David Yost)....Pages 177-182 Spectral Triples on ON (Magnus Goffeng, Bram Mesland)....Pages 183-201 Application of Semifinite Index Theory to Weak Topological Phases (Chris Bourne, Hermann Schulz-Baldes)....Pages 203-227 Filtered K-Theory for Graph Algebras (Søren Eilers, Gunnar Restorff, Efren Ruiz, Adam P. W. Sørensen)....Pages 229-249 Gysin Exact Sequences for Quantum Weighted Lens Spaces (Francesca Arici)....Pages 251-262 A Signed Version of Putnam’s Homology Theory: Lefschetz and Zeta Functions (Robin J. Deeley)....Pages 263-276 A Simple Model of 4d-TQFT (Rinat Kashaev)....Pages 277-286 Morse Structures on Partial Open Books with Extendable Monodromy (Joan E. Licata, Daniel V. Mathews)....Pages 287-303 Counting Belyi Pairs over Finite Fields (George Shabat)....Pages 305-322 Unravelling the Dodecahedral Spaces (Jonathan Spreer, Stephan Tillmann)....Pages 323-347 Front Matter ....Pages 349-349 Lecture Notes on Infinity-Properads (Philip Hackney, Marcy Robertson)....Pages 351-374 Lectures on Feynman Categories (Ralph M. Kaufmann)....Pages 375-438 Moduli Spaces of (Bi)algebra Structures in Topology and Geometry (Sinan Yalin)....Pages 439-488 Embedding Calculus and the Little Discs Operads (Victor Turchin)....Pages 489-500 Groups of Automorphisms and Almost Automorphisms of Trees: Subgroups and Dynamics (Adrien Le Boudec)....Pages 501-523 Normal Subgroup Structure of Totally Disconnected Locally Compact Groups (Colin D. Reid)....Pages 525-560 Automorphism Groups of Combinatorial Structures (Anne Thomas)....Pages 561-592 A Survey of Elementary Totally Disconnected Locally Compact Groups (Phillip Wesolek)....Pages 593-611 The Scale, Tidy Subgroups and Flat Groups (George Willis)....Pages 613-636 Introduction to Quantum Invariants of Knots (Roland van der Veen)....Pages 637-656 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