Systolic and Diastolic Geometry - How Packing Simplices Helps to Study Symplectic Systoles

Watch this lecture titled "How packing simplices helps to study symplectic systoles" delivered by Alexey Balitskiy from Luxembourg at the "Systolic and Diastolic Geometry" event organized by the Instituto de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro. The 59-minute talk explores the relationship between packing simplices and symplectic systoles, contributing to the broader field of geometric comparison problems that examine relationships between volumes of spaces and lengths/areas of curves/surfaces they contain. This lecture was part of a larger event featuring international speakers discussing topics in Differential Geometry, Analysis, and Symplectic Geometry, addressing fundamental questions such as optimal inequalities for periodic orbits in convex billiards, lengths of shortest geodesics on spheres, and eigenvalues of Laplacian operators on surfaces. The event aimed to present the state of the art on major conjectures in Geometric Analysis and Symplectic Geometry while bringing together specialists to inspire innovative approaches to solving fundamental problems in these fields.