This talk will report on the work of Simon Schieder, a graduate student at Harvard. Let X be a smooth projective curve and G a reductive group. We consider the moduli stack Bun_G that classifies G-bundles on X. The diagonal morphism Bun_G->Bun_G\times Bun_G admits a canonical compactification, which is a tool to handle problems that are caused by the fact that Bun_G has "horns". Let us denote this compactification by \bar{Bun}_G. In this talk we will be interested in the intersection cohomology sheaf of \bar{Bun}_G, and some related questions. We will see that what encodes the answer to such questions is the phenomenon of "Picard-Lefschetz oscillators".