I will talk about the recent progress on the DK conjecture connecting birational geometry and the
derived categories, and related conjectures such as DL conjecture, etc. I will also discuss two kinds of
factorizations of birational maps; those into flips, flops and divisorial contractions according to the
minimal model programme, and more traditional factorizations into blow-ups and blow-downs with
smooth centres.
This video is part of Harvard University‘s conference JDG 2017.
