Dear all, Sveta Makarova (ANU) will give a talk for this month's PCT seminar (https://pctseminar.github.io/<https://pctseminar.github.io>) on Friday August 7 at 10am JST/11am AED (1am UTC). The zoom link to join the seminar is: https://kyoto-u-edu.zoom.us/j/82401794000?pwd=VjVmzVjmlgxhkdHES4xYeQBTpMzQkS... Title: Contractions and flops via moduli of non-pure sheaves Abstract: The goal of the talk is to convince the audience that 2-categorical enhancements of some classical geometric objects yield interesting geometric constructions. Consider the stack of ideal sheaves of l points on a smooth projective variety X. Its good moduli space is the well-known Hilbert scheme of l points Hilb^l(X). In this talk, I will define a certain enlargement U of this stack and prove that it admits a good moduli space. Furthermore, I will describe a different open substack of U that admits a good moduli space and explain how it yields a surgery diagram via non-GIT wall-crossing. As an application in the toy case l=1, I will explain how this construction helps contract rational curves on higher-dimensional varieties and, time permitting, use the interpretation of the surgery as a fine moduli of sheaves to prove instances Kawamata’s DK-hypothesis in this setting. This is joint work with Andres Fernandez Herrero. We hope to see you there! If you cannot make it, talks after posted on youtube afterwards: https://www.youtube.com/@PCTSeminar Best wishes, Soichiro Fujii, Zeinab Galal, JS Lemay