Abstract
In 957 Eugenio Calabi conjectured, that a compact Kähler manifold $M$ has a unique Kähler metric in the same class whose Ricci form is any given 2-form representing the first Chern class of $M$.
The conjecture was solved two decades later by Shing-Tung Yau. by constructing a solution of the associated complex Monge-Ampère equation using the continuity method.
In the seminar I will give an overview of the Calabi-Yau Theorem and its generalizations in symplectic and Hermitian geometry.
