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Monday, February 16, 2015

**Abstract:** “Quiver” is the name that geometers and representation theorists give to finite directed graphs. A representation of a quiver is a diagram in the category of vector spaces that is shaped like the quiver in the obvious sense, and an algebraic geometer may have many reasons to consider categories of such representations. One goal of this talk is to highlight some of these reasons; the other is to walk the then-hopefully-motivated audience through Nakajima’s construction of moduli spaces of quiver representations. Here, a formidable list of characters from the world of quotients appear—GIT, stability conditions, the moment map, and Hamiltonian reduction—but in the tractable setting of affine schemes and vector spaces, and this talk can be viewed as a petting zoo encounter with these ideas.