David Rydh: Functorial flatification of maps by blow-ups

There are several slightly different results on flatification of maps and modules by blow-ups, e.g., by Raynaud-Gruson, Hironaka, Nagata, Oneto-Zatini, Villamayor, Fujiwara-Kato and Sædén-Ståhl. I will give a quick survey of some of these results and describe a new variant of the construction of Hironaka that is functorial with respect to flat maps. A key ingredient is to understand monomorphisms that are not locally closed immersions.