Vanishing theorem for the cohomology of line bundles on Bott-Samelson   varieties
  We use the toric degeneration of Bott-Samelson varieties and the description of cohomolgy of line bundles on toric varieties to deduce vanishings results for the cohomology of lines bundles on Bott-Samelson varieties. 
Boris Pasquier (HCM, Bonn)