Simplicial Methods for Operads and Algebraic Geometry

Author: Ieke Moerdijk,Bertrand Toën

Publisher: Springer Science & Business Media

ISBN: 3034800525

Category: Mathematics

Page: 186

View: 5827

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This book is an introduction to two new topics in homotopy theory: Dendroidal Sets (by Ieke Moerdijk) and Derived Algebraic Geometry (by Bertrand Toën). The category of dendroidal sets is an extension of that of simplicial sets, based on rooted trees instead of linear orders, suitable as a model category for higher topological structures. Derived algebraic geometry deals with functors from simplicial commutative rings to simplicial sets subject to a homotopical descent condition. The material in the book is an enhanced version of lecture notes from courses given within a special year on Homotopy Theory and Higher Categories at the CRM in Barcelona.
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Infinity Properads and Infinity Wheeled Properads

Author: Philip Hackney,Marcy Robertson,Donald Yau

Publisher: Springer

ISBN: 3319205471

Category: Mathematics

Page: 358

View: 342

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The topic of this book sits at the interface of the theory of higher categories (in the guise of (∞,1)-categories) and the theory of properads. Properads are devices more general than operads and enable one to encode bialgebraic, rather than just (co)algebraic, structures. The text extends both the Joyal-Lurie approach to higher categories and the Cisinski-Moerdijk-Weiss approach to higher operads, and provides a foundation for a broad study of the homotopy theory of properads. This work also serves as a complete guide to the generalised graphs which are pervasive in the study of operads and properads. A preliminary list of potential applications and extensions comprises the final chapter. Infinity Properads and Infinity Wheeled Properads is written for mathematicians in the fields of topology, algebra, category theory, and related areas. It is written roughly at the second year graduate level, and assumes a basic knowledge of category theory.
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2016 MATRIX Annals

Author: Jan de Gier,Cheryl E. Praeger,Terence Tao

Publisher: Springer

ISBN: 3319722999

Category: Mathematics

Page: 656

View: 4760

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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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