Introduction to Systolic Geometry - Lecture 2

Explore systolic geometry in this 55-minute mathematics lecture that introduces the concept of systole in Riemannian manifolds - the length of the shortest non-contractible loop - and examines methods for determining its upper bounds relative to manifold volume. Learn about Loewner's pioneering 1949 work with torus systoles and follow the evolution through Berger's 1960s questions about aspherical manifolds. Delve into two significant Gromov results: Kodani's proof for systole upper bounds in high genus surfaces and Nabutovsky's recent proof establishing improved constants for aspherical manifold systole bounds.