Appears in collection : Jean-Morlet Chair 2021 - Conference: Faces of Singularity Theory / Chaire Jean-Morlet 2021 - Conférence : Visages de la théorie des singularités

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.