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2016 MATRIX annals

Author: David R Wood; Jan de Gier; Cheryl E Praeger; Terence Tao
Publisher: Cham, Switzerland : Springer, 2018.
Series: MATRIX book series, 1.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: David R Wood; Jan de Gier; Cheryl E Praeger; Terence Tao
ISBN: 9783319722993 3319722999 3319722980 9783319722986
OCLC Number: 1031214412
Description: 1 online resource.
Contents: Intro; Preface; 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; Contents; Part I Refereed Articles; Homotopical Properties of the Simplicial Maurer-Cartan Functor; 1 Introduction; 2 Preliminaries; 2.1 Filtered L∞-Algebras; 2.2 Maurer-Cartan Elements; 2.3 Getzler-Hinich Construction; 3 The Functor sMC(-) Preserves Weak Equivalences and Fibrations 4 Homotopy Transfer TheoremReferences; Fibrations in ∞-Category Theory; 1 Introduction; 2 Left, Right, and Kan Fibrations; 3 Inner Fibrations and Isofibrations; 4 Cocartesian and Cartesian Fibrations; 5 Flat Inner Fibrations; 6 Marked Simplicial Sets and Categorical Patterns; 7 Constructing Fibrations via Additional Functoriality; References; The Smooth Hom-Stack of an Orbifold; References; Complicial Sets, an Overture; 1 Introduction; 2 Introducing Complicial Sets; 2.1 Quasi-Categories as (∞,1)-Categories; 2.2 Towards a Simplicial Model of (∞,2)-Categories; 2.3 Stratified Simplicial Sets 3 Words and Their Cooperads3.1 Words; 3.2 The Word Cooperad; 3.3 The Non-crossing Word Cooperad; 4 Review of (Homotopy) Probability Theory; 4.1 Review of Homotopy Probability Theory; 4.2 Review of Free Cumulants; 5 The Non-crossing Word Cooperad and Free Probability Theory; References; Endomorphisms of Lie Groups over Local Fields; 1 Introduction; 2 Some Basics of Totally Disconnected Groups; 3 Endomorphisms of K-Vector Spaces; 4 Analytic Functions, Manifolds and Lie Groups; 5 Construction of Small Open Subgroups; 6 Endomorphisms of p-Adic Lie Groups; 7 Invariant Manifolds Around Fixed Points. 8 Endomorphisms of Lie Groups over K9 Contractive Automorphisms; 10 Expansive Automorphisms; 11 Distality and Lie Groups of Type R; References; Compact Convex Sets with Prescribed Facial Dimensions; 1 Introduction; 2 Main Result; 3 Fractal Convex Sets; References; Chebyshev Multivariate Polynomial Approximation: Alternance Interpretation; 1 Introduction; 2 Optimality Conditions; 2.1 Convexity of the Objective; 2.2 Optimality Conditions: General Case; 2.3 Optimality Conditions for Multivariate Linear Functions; 3 Conclusions and Further Research Directions; References; Spectral Triples on ON.
Series Title: MATRIX book series, 1.
Responsibility: David R. Wood, editor-in-chief ; Jan de Gier, Cheryl E. Praeger, Terence Tao, editors.

Abstract:

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.

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