EAN: 9783319701561

ADVANCED COURSES IN MATHEMATICS - CRM BARCELONA...

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.

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