Systolic and Diastolic Geometry - Min-max Widths Compared to Other Geometric Invariants

Explore a lecture by Rafael Montezuma from the Federal University of Ceará (UFC) on "Min-max widths compared to other geometric invariants" as part of the Systolic and Diastolic Geometry event held at IMPA, Rio de Janeiro. This one-hour talk examines the relationship between geometric volume and the length/area of curves/surfaces within spaces. The lecture addresses fundamental questions in geometric analysis, such as: which bounded convex billiards with fixed area contain the largest minimum-period orbit? Among spheres of equal area, how large can the length of the shortest immersed periodic geodesic be? The presentation is part of a broader event featuring international speakers discussing systolic inequalities, minimal surfaces, and geometric analysis. The event aims to share current research on key conjectures in these fields and foster collaboration between different mathematical specialties to advance fundamental problems in Geometric Analysis and Symplectic Geometry.