Résumé : In this talk I discuss a fast canonical method of resolving any singularities in characteristic zero. The method uses the, introduced here, operation of bordent expansion analogous to smooth (stack theoretic) weighted blow-ups considered in the joint paper with Abramovich-Temkin-Wlodarczyk and independently by McQuillan. The method is done in the language of smooth ambient schemes with torus actions.

Keywords : weighted blow-up