BunG and Higgs Bundles - Moduli Stacks and Geometric Langlands - Talk 4

Explore an advanced mathematics seminar talk that delves into moduli stacks and their relationship with Bun_G and Higgs bundles. Begin with a comprehensive examination of moduli stacks that parametrize objects of categories and understand how Bun_G fits within this framework. Learn about the fundamental concepts of tangent, cotangent, and inertia stacks of a stack X, and discover their interpretations as vector bundle stacks. Examine the detailed description of tangent/cotangent stacks of moduli stacks, leading to the important isomorphism between the cotangent stack of Bun_G and Higgs bundles. Gain insights into the concrete geometry of Higgs bundles, with particular emphasis on the 'global nilpotent cone' and its significance in Geometric Langlands theory.