Some classification results for complete Kahler-Ricci solitons

 Ricci solitons are singularity models in Ricci flow, so it is important to classify them. I will talk about some classification results of complete Kahler-Ricci solitons. In particular, we show that the example constructed by Feldman-Ilmanen-Knopf is the only non-trivial shrinking gradient Kahler-Ricci soliton in dimension 4 which is conical at infinity. This talk is based on the preprint axiv:1904.00147, which is joint work with R. Conlon and A. Deruelle.