Colloquium DATE 2017-10-13¡@14:10-15:00 PLACE ¼Æ¾ÇÀ]3174±Ð«Ç SPEAKER ³¯¥¿³Ç§U²z±Ð±Â¡]¤¤¥¡¤j¾Ç¼Æ¾Ç¨t¡^ TITLE A Generalization of Kawamata Blowup in Higher Dimension ABSTRACT In this talk, we would introduce some basic facts about cyclic quotient singularities and discuss about some divisorial contractions in dimension $3$. Then, we show that the divisorial contraction to a terminal cyclic quotient singularity of index $r$ with minimal discrepancy $1/r$ is unique. This generalizes a result of Kawamata to higher dimension. However, there exist some terminal cyclic quotient singularities $(X,P)$ with minimal discrepancy $>1/r$ which allows infinitely many divisorial contractions to $(X,P)$.