Algebraic Geometry Student's Seminar - How to take quotients in Algebraic Geometry? (aka Geometric Invariant Theory)

Unlike point-set topology, taking quotients in Algebraic Geometry is not so simple. Finding the correct formulation of taking quotients in Algebraic Geometry (aka Geometric Invariant Theory or GIT) has led to a lot of important research, some of which include the construction of several moduli spaces (such as moduli space of vector bundles on a curve, or moduli of genus g smooth curves etc) and the more recent development of variation of GIT and its link to birational geometry. In this talk I will try to give a brief exposition of this theory with some applications.