Singularities in positive characteristic, stratification and   simplification of the singular locus
  We introduce an upper semi-continuous function that stratifies the highest multiplicity locus of a hypersurface in arbitrary characteristic (over a perfect field). The blow-up along the maximum stratum defined by this function leads to a form of simplification of the singularities, also known as a reduction to the monomial case. 
Ana Bravo (Universidad Aut\'onoma de Madrid), Orlando Villamayor   (Universidad Aut\'onoma de Madrid)