Speaker: Luis Atzin
University of Notre Dame
Will give a Graduate Student Seminar entitled:
Classifying non-negatively curved 4-manifolds
Abstract: Manifolds with positive or nonnegative sectional curvature are important and interesting mathematical objects. Some fundamental results, like Gromov’s Betti number Theorem, Bonnet–Myers or Synge’s Theorem have helped understand the topology of these manifolds. However, we are far from being able to classify all of them. A classification of these manifolds in lower dimensions has been proven successful in the case when they have a large group of isometries. In this talk we will give a sketch of the proof of the classification of all closed, simply-connected, nonnegatively curved 4-manifolds with circle symmetry. This will lead us to a crash course in Alexandrov geometry, a pivotal tool essential for the proof. We will also see that the classification eventually boils down to showing that some curve in the 3-sphere is the unknotted.
Date: 10-03-2024
Time: 2:00 pm
Location: 258 Hurley Hall