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The Resource 2016 MATRIX annals, David R. Wood, editor-in-chief ; Jan de Gier, Cheryl E. Praeger, Terence Tao, editors, (electronic book)

2016 MATRIX annals, David R. Wood, editor-in-chief ; Jan de Gier, Cheryl E. Praeger, Terence Tao, editors, (electronic book)

Editor
Contributor
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 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
Language
eng
Work
Publication
Extent
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
Isbn
9783319722993
Instance
Label
2016 MATRIX annals
Title
2016 MATRIX annals
Statement of responsibility
David R. Wood, editor-in-chief ; Jan de Gier, Cheryl E. Praeger, Terence Tao, editors
Contributor
Editor
Subject
Language
eng
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 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
Member of
Cataloging source
N$T
Dewey number
510.71
Index
no index present
LC call number
QA11.A1
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorDate
  • 1948-
  • 1975-
http://library.link/vocab/relatedWorkOrContributorName
  • Wood, David R.
  • Gier, Jan de
  • Praeger, Cheryl E.
  • Tao, Terence
http://library.link/vocab/subjectName
  • Mathematics
  • K-Theory
  • Topology
Label
2016 MATRIX annals, David R. Wood, editor-in-chief ; Jan de Gier, Cheryl E. Praeger, Terence Tao, editors, (electronic book)
Instantiates
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Extent
1 online resource.
Form of item
online
Isbn
9783319722993
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-72299-3
System control number
  • (OCoLC)1031214412
  • on1031214412
Label
2016 MATRIX annals, David R. Wood, editor-in-chief ; Jan de Gier, Cheryl E. Praeger, Terence Tao, editors, (electronic book)
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Extent
1 online resource.
Form of item
online
Isbn
9783319722993
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-72299-3
System control number
  • (OCoLC)1031214412
  • on1031214412

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