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Monday, October 5, 2015

**Abstract:** Classification of vector bundles is an important problem in algebraic geometry. It naturally leads to the study of moduli spaces of bundles. To obtain a nice scheme structure for the moduli spaces, one restricts the objects of interest to semistable bundles. Through the compactification of the moduli spaces, one naturally encounters non-locally free sheaves. In this talk, we will introduce a geometric construction of moduli spaces of semistable sheaves. By showing stability condition for coherent sheaves and stable points in the GIT sense amount to the same constraint, we construct the moduli space of semistable sheaves as a GIT quotient of an open subscheme of the Quot-scheme.