Monge-Ampère equations arise in many areas of math, most notably in differential geometry, optimal transport and fluid dynamics. In this talk, we will focus on the Dirichlet problem for the complex Monge-Ampère equation in a strictly pseudoconvex domain with continuous data. After briefly recalling how Perron method works for finding the solution to the classical Laplacian equation, we will see how the same method leads to the solution to the Dirichlet problem for the complex Monge-Ampère equation. Time permitting, we will also briefly mention what Monge-Ampère type equations look like in a more general setup, e.g. on complex manifolds or over different ground fields, and explore how they relate to the geometry of Kähler manifolds, or more generally the geometry of projective varieties. No background in pdes or several complex variables will be assumed. Speaker(s): Yueqiao Wu (University of Michigan)