A canonical degeneration of the moduli space of bundles
--Simon Schieder, December 11, 2015

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We study the singularities of the Drinfeld-Lafforgue-Vinberg
compactification of the moduli space of G-bundles on a smooth
projective curve for a reductive group G. The definition of this
compactification is due to Drinfeld and relies on the Vinberg
semigroup of G. We will mostly focus on the case G=SL<sub>2</sub>; in this case
the discussion can be made very concrete and entirely geometric; in
particular, no background in representation theory, number theory, or
the geometric Langlands program is assumed. For G=SL<sub>2</sub> the
compactification can alternatively be viewed as a canonical
one-parameter degeneration of the moduli space of SL<sub>2</sub>-bundles. We
study the singularities of this one-parameter degeneration via its
nearby cycles. Time permitting, we might briefly mention a
generalization to the case of an arbitrary reductive group G, the
relationship with the geometric Langlands program, as well as
applications in number theory and representation theory.