Systolic and Diastolic Geometry - Growth of k-dimensional Systoles in Congruence Coverings

Explore a 58-minute lecture by Mikhail Belolipetsky from IMPA (Instituto de Matemática Pura e Aplicada) on "Growth of k-dimensional systoles in congruence coverings" as part of the "Systolic and Diastolic Geometry" event held in Rio de Janeiro. The lecture delves into geometric problems comparing the volume of spaces with the length/area of curves/surfaces they contain, addressing fundamental questions in Differential Geometry, Analysis, and Symplectic Geometry. Learn about systolic inequalities, periodic geodesics, Laplacian eigenvalues, and other related concepts that connect various mathematical specialties. This presentation was part of a broader conference featuring international speakers discussing cutting-edge research in Geometric Analysis and Symplectic Geometry, with the goal of motivating innovative approaches to solve fundamental problems in these fields.