Explore a 32-minute short talk by Brayan Cuzzuol Ferreira from UFES titled "From symplectic embeddings to systolic inequalities on the sphere," presented at the Systolic and Diastolic Geometry event at IMPA, Rio de Janeiro. The talk examines the relationship between symplectic geometry and systolic inequalities, contributing to the broader discussion of geometric comparison problems between volume of spaces and length/area of curves/surfaces. Part of a larger conference featuring international speakers addressing fundamental problems in Geometric Analysis and Symplectic Geometry, this presentation connects with themes like periodic orbits in convex billiards, geodesics on spheres, and Laplacian eigenvalue problems. The talk is delivered in Portuguese and is part of IMPA's collection of mathematical research presentations.