Effective Testing in Complex Geometry

The project will pioneer a new strategy to test the solvability of geometric partial differential equations in practice, reducing abstract and often impossible-to-test theoretical criteria to concrete conditions that for the first time can be widely tested using a computer. As an application, we will strive to theoretically deepen our understanding of complex geometric shapes generalizing those arising from Einstein's field equations in physics. The project will fund two postdocs and one Ph.D. student.