Research Seminar: Resolution of singularities

We will study the new results by Abramovich, Temkin and Włodarczyk on resolution of singularities over a field $k$ of characteristic $0$. Their work, combined with a “destackification theorem” by Bergh gives a new proof of Hironaka’s celebrated theorem. If one is willing to “stay in the world of stacks”, one obtains resolution with additional nice features (functoriality, and the resolution is given by a straight-forward process where one defines an invariant at each point which says “how singular” the point is, and at each step the maximum of the invariant drops after a suitable “stacky weighted blow-up”.

Program: pdf (updated Oct. 10)