Valley Geometry Seminar: Kai Xu (Harvard)

Abstract. I will talk about my recent construction of semiorthogonal decompositions of moduli of principal bundles on a curve into its symmetric powers, for both the moduli stack of all G-bundles and the coarse moduli space of semistable G-bundles. 

The essential ingredients in the proof include Borel-Weil-Bott theory for loop groups, highest weight structure of current group representation, derived Θ-stratification and local-global compatibility of Kac-Moody localization. 

For the full moduli stack of all G-bundles the decomposition we construct is complete, while for the coarse moduli space of semistable G-bundles it is not clear in full generality yet.