Geometric Analysis and Topology Seminar

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Complete Riemannian 4-manifolds with uniformly positive scalar curvature metric

Speaker: Anubhav Mukherjee, Princeton University

Location: Warren Weaver Hall 512

Date: Friday, October 18, 2024, 11 a.m.

Synopsis:

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 Chodos 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.