Edward Bierstone

Abstract:   Algorithms for resolution of singularities in characteristic zero (by Bierstone-Milman, Villamayor and, more recently, Wlodarczyk and Kollar) are based on Hironaka's idea of reducing the problem to a simpler question of desingularization of an "idealistic exponent" or "marked ideal". How can we determine whether two marked ideals undergo the same resolution process? From the point of view of this question of functoriality or equisingularity, I will compare algorithms and discuss results and open problems.