  Let G be a reductive group and let Bun_G denote the moduli stack of G-bundles
on a smooth projective curve. We begin the study of the singularities of a
canonical compactification of Bun_G due to V. Drinfeld (unpublished), which we
refer to as the Drinfeld-Lafforgue-Vinberg compactification. For G=GL_n certain
smooth open substacks of this compactification have already appeared in the
work of Drinfeld and of L. Lafforgue on the Langlands correspondence for
function fields. The Drinfeld-Lafforgue-Vinberg compactification is however
already singular for G=SL_2; questions about its singularities arise naturally
in the geometric Langlands program, and form the topic of the present article.
  Drinfeld's definition of the compactification for a general reductive group G
relies on the Vinberg semigroup of G, and will be given in [Sch]. In the
present paper we focus on the case G=SL_2. In this case the compactification
can alternatively be viewed as a canonical one-parameter degeneration of the
moduli space of SL_2-bundles. We study the singularities of this degeneration
via the weight-monodromy theory of its nearby cycles: We give an explicit
description of the nearby cycles sheaf in terms of certain novel perverse
sheaves which we call "Picard-Lefschetz oscillators" and which govern the
singularities of the degeneration. We then use this description to determine
its intersection cohomology sheaf and other invariants of its singularities.
  We also discuss the relationship of our results for G=SL_2 with the
miraculous duality of Drinfeld and Gaitsgory in the geometric Langlands
program, as well as two applications of our results to the classical theory: To
Drinfeld's and Wang's "strange" invariant bilinear form on the space of
automorphic forms; and to the categorification of the Bernstein asymptotics map
studied by Bezrukavnikov and Kazhdan as well as by Sakellaridis and Venkatesh.
