Introduction to Systolic Geometry - Lecture 3

Learn about systolic geometry in this one-hour lecture that explores the fundamental concepts of systole in Riemannian manifolds and its relationship to volume. Discover the historical progression from Loewner's 1949 breakthrough with torus to Berger's questions about aspherical manifolds in the 1960s. Delve into two significant Gromov results: examine Kodani's proof for the upper bound of systole in high genus surfaces, and explore Nabutovsky's recent proof establishing improved constants for systole bounds in aspherical manifolds.