The stringy motivic measure and singularities

Abstract:There are  two different motivic measures on a singular variety X which generalize the motivic measure on smooth algebraic varieties suggested by Kontsevich. The motivic measure introduced by Denef and Loeser puts no restriction on singularities of X. Another motivic measure was inspired  by the string theory. In contrast to the Denef-Loeser motivic measure the stringy motivic measure was defined only for an algebraic variety X  with at worst Q-Gorenstein log-terminal singularities. The purpose of the talk is to explain applications of the stringy motivic measure and some open questions related to singularities of algebraic varieties.