Abstract: In this talk, we will discuss various notions of dualities in commutative algebra, which offer a powerful homological tool to understand the properties of various classes of rings and modules. In particular, we will focus on algebraic linkage, which is the algebraic counterpart of liaison theory in algebraic geometry, explaining how it can be used to study free resolutions. The talk will be expository, so graduate students interested in algebra or algebraic geometry are encouraged to attend.
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