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Graduate Student Geometry-Topology Seminar

Monday, October 17, 2022 - 4:30pm

Jacob van Hook



University of Pennsylvania

DRL math lounge (4E17)

One of the fundamental geometric properties of a manifold is its curvature. For surfaces this is the traditional Gauss curvature—at every point we may assign a number—but higher dimensional manifolds can have more complicated behavior. For instance, at a given point there may be some directions which "look flat" while other directions don't. I will discuss this and some known results about manifolds which are "flat" in many, but not all, directions.