Infinitesimal Structure of BunG and Jet Spaces - Talk 11

Explore an advanced mathematics seminar talk examining the infinitesimal structure of principal G-bundles and jet spaces in algebraic geometry. Delve into detailed explanations of jet spaces containing germs of regular functions on Bun_G(X) over a principal G-bundle P on smooth projective curves. Learn how the fiber of differential operators' sheaf on BunG relates to these structures through Beilinson-Ginzburg and Beilinson-Drinfeld's explicit descriptions. Understand the connection between first-order jet spaces, cotangent spaces, and their extension to higher-order jets, discovering how conformal blocks for Kac-Moody algebras emerge naturally in this context. Follow along as the main theorem describing jets is demonstrated using residue pairing techniques.