Authors:
Editors:
- Offers a unique combination of exciting new topics in the crossroad between commutative algebra, representation theory and homotopy theory
- Provides a great introduction to higher hall algebras
- Presents a self-contained introduction, with illustrative examples, to the translation of classical commutative algebra concepts to homotopy theory
Part of the book series: Advanced Courses in Mathematics - CRM Barcelona (ACMBIRK)
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Table of contents (4 chapters)
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Front Matter
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Back Matter
About this book
This volume presents an elaborated version of lecture notes for two advanced courses: (Re)Emerging methods in Commutative Algebra and Representation Theory and Building Bridges Between Algebra and Topology, held at the CRM in the spring of 2015.
Homological algebra is a rich and ubiquitous area; it is both an active field of research and a widespread toolbox for many mathematicians. Together, these notes introduce recent applications and interactions of homological methods in commutative algebra, representation theory and topology, narrowing the gap between specialists from different areas wishing to acquaint themselves with a rapidly growing field. The covered topics range from a fresh introduction to the growing area of support theory for triangulated categories to the striking consequences of the formulation in the homotopy theory of classical concepts in commutative algebra. Moreover, they also include a higher categories view of Hall algebras and an introduction to the use of idempotent functors in algebra and topology.
Authors, Editors and Affiliations
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Matemàtiques, Eix Central, Universitat Autònoma de Barcelona Matemàtiques, Eix Central, Bellaterra, Barcelona, Spain
Dolors Herbera
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Departament de Matemàtiques, Universitat Autònoma de Barcelona Departament de Matemàtiques, Bellaterra, Spain
Wolfgang Pitsch
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Matemàtiques i Informàtica, Universitat de Barcelona Matemàtiques i Informàtica, Barcelona, Spain
Santiago Zarzuela
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Department of Mathematics, Kungliga Teknisk Högskola (KTH), Stockolm, Sweden
Wojciech Chachólski
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Hausdorff Center for Mathematics, Bonn, Germany
Tobias Dyckerhoff
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School of Mathematics and Statistics, University of Sheffield, Sheffield, United Kingdom
John Greenlees
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Fakultät für Mathematik, Universität Bielefeld, Bielefeld, Germany
Greg Stevenson
About the editors
Tobias Dyckerhoff is a Junior Fellow at the Hausdorff Center for Mathematics in Bonn, Germany.
Greg Stevenson is a Research Assistant at the Bielefeld University in Germany.
John Greenlees is a Professor at the The University of Sheffield in the United Kingdom.
Wojciech Chachólski is a Professor at the KTH Royal Institute of Technology in Stockholm, Sweden.
Bibliographic Information
Book Title: Building Bridges Between Algebra and Topology
Authors: Wojciech Chachólski, Tobias Dyckerhoff, John Greenlees, Greg Stevenson
Editors: Dolors Herbera, Wolfgang Pitsch, Santiago Zarzuela
Series Title: Advanced Courses in Mathematics - CRM Barcelona
DOI: https://doi.org/10.1007/978-3-319-70157-8
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Softcover ISBN: 978-3-319-70156-1Published: 13 April 2018
eBook ISBN: 978-3-319-70157-8Published: 31 March 2018
Series ISSN: 2297-0304
Series E-ISSN: 2297-0312
Edition Number: 1
Number of Pages: XIII, 225
Topics: Commutative Rings and Algebras, Associative Rings and Algebras, Category Theory, Homological Algebra, Algebraic Topology