V. Balaji (Chennai): Principal bundles and the Donaldson-Uhlenbeck compactification
 
 Let $H$ be a semisimple algebraic group. We prove the semistable
  reduction theorem for $\mu$--semistable principal $H$--bundles over
  a {\it smooth projective variety $X$} defined over the field $\bc$.
  When $X$ is a {\it smooth projective surface} and $H$ is simple, we
  construct the algebro--geometric Donaldson--Uhlenbeck
  compactification of the moduli space of $\mu$--semistable principal
  $H$--bundles with fixed characteristic classes and describe its
  points.  For large characteristic classes we show that the moduli
  space of $\mu$--stable principal $H$--bundles is non--empty.