Title: Local singularities of planar plurisubharmonic functions.

Abstract: I will present joint work with Charles Favre, in which we use valuations to study the logarithmic singularity of a local plurisubharmonic function in dimension 2. The Lelong number and Kiselman numbers are examples of valuations, whereas every generalized Lelong number in the sense of Demailly (under some regularity conditions) decomposes canonically as an average of valuations. In a sense that will be made precise, valuations capture essentially all the information on the singularity.