Appears in collection : Not Only Scalar Curvature Seminar

In three dimensions, geometry plays a crucial role in classifying the topology of manifolds. Inspired by this, we set out to explore the intricate world of smooth 4-manifolds through the lens of geometry. Specifically, we aim to understand under what conditions a contractible 4-manifold admits a uniform positive scalar curvature metric. In collaboration with Otis Chodosh and Davi Maximo, we demonstrated that in certain cases, the existence of such a metric can provide insight into the topology of 4-manifolds. Moreover, by utilizing Floer theory, we identified obstructions to the existence of such metrics in 4-manifolds.