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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;
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.
Higher Categorical Aspects of Hall Algebras.- Support Theory for Triangulated Categories.- Homotopy Invariant Commutative Algebra over Fields.- Idempotent Symmetries in Algebra and Topology.