Nonnegative Ricci Curvature, Nilpotency, and Hausdorff Dimension

Nonnegative Ricci Curvature, Nilpotency, and Hausdorff Dimension

Explore a mathematical lecture on nonnegative Ricci curvature, nilpotency, and Hausdorff dimension presented by Jiayin Pan from UC Santa Cruz at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the geometric features of Nabonnand-type examples and their universal covers, examining how minimal representing loops of π₁(M,p) escape from bounded sets. Investigate the resulting wild limit orbits in the asymptotic cones of M̃, focusing on their non-convexity and large Hausdorff dimension. Analyze the relationships between the escape phenomenon, orbits in asymptotic cones, and the virtual abelianness or nilpotency of fundamental groups in this hour-long presentation that builds upon Wei's previous talk.