Title: Line bundles on the moduli of parahoric bundles

Abstract: Moduli spaces of vector bundles over a curve X have been a central focus in algebraic geometry and adjacent fields. A natural generalization of these spaces can be obtained by replacing vector bundles with G-bundles, for G an algebraic group. In this talk I focus on the case when G takes the form of a parahoric Bruhat-Tits group and discuss how, using representation-theoretical methods, one can describe the Picard group of Bun_G, the moduli space of G-bundles. Specifically, I show how twisted conformal blocks can be used to detect when line bundles on an appropriate flag variety descend to Bun_G. This is based on joint work with J. Hong.