Conference talk on stability of systolic inequalities for the Klein bottle presented by Jan Eyll from Ruhr-Universität Bochum at the "Systolic and Diastolic Geometry" event hosted by IMPA (Instituto de Matemática Pura e Aplicada) in Rio de Janeiro. Explore geometric problems comparing volume of spaces with lengths/areas of curves/surfaces they contain, focusing specifically on systolic inequalities for the Klein bottle. This 32-minute presentation was part of a larger mathematical conference featuring international speakers discussing topics in Geometric Analysis and Symplectic Geometry, including systolic inequalities in Reeb dynamics, minimal surfaces, and spectral optimization. The event aimed to share current research on fundamental conjectures and foster collaboration between different mathematical specialties to advance significant problems in the field.