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Explore a mathematical lecture that delves into the principles of quantitative geometry and its application to geodesics, presented by Isabel Beach from the University of Toronto at the Hausdorff Center for Mathematics. Learn about effective versions of existence theorems for geometric objects, with particular focus on Serre's proof regarding infinite geodesics connecting points on closed Riemannian manifolds. Examine current quantitative theorems about geodesics and their proof methodologies, including recent developments in the study of "short" geodesics intersecting submanifolds at right angles. Gain insights into how length bounds for geodesics can be established and understand their significance in modern geometric analysis during this 53-minute presentation.
