Tilting theory and cluster combinatorics (Idun Reiten)
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In the first lecture we discuss basic properties and results from
the theory of cluster algebras of Fomin-Zelevinsky. In the second
lecture we introduce and discuss cluster categories. In particular we
talk about (cluster)-tilting theory and make comparison with ordinary
tilting theory.  In the third lecture we discuss various properties of
the associated cluster-tilted algebras, and compare with tilted
algebras. Then we give some applications to cluster algebras in the
last lecture.