Complex Algebraic Geometry

In Lafforgue's proof of the Langlands conjecture for GL(2) over a functional field, an important step is to compactify the moduli spaces of Drinfeld's shtukas. In this talk, I will present a new approach to this problem using the Geometric Invariant Theory. If time permits, I will present how to extend this method to compactify moduli spaces of G-shtukas for a split reductive group G.