Writing Milestone Seminar: Yau's proof of the Calabi Conjecture

Given a compact complex M manifold there is in general no natural choice metric. A natural question is to ask what is the ``best'' metric we can endow on M. In the 50's, the differential geometer Eugenio Calabi studied this question and through considering various curvature notions made a conjecture on the existence of a special class of metrics called Kähler-Einstein metrics. In 1978, Yau definitively proved the conjecture using geometric analysis. This talk will be expository and cover this beautiful topic.