Explore a 53-minute mathematics lecture from the ESI's Thematic Programme on "Infinite-dimensional Geometry: Theory and Applications" that delves into the Willmore energy functional and its application to surface geometry. Learn about this conformally invariant functional that measures the total bending of immersed surfaces in Euclidean space, with particular focus on tori with prescribed conformal class. Discover the analysis of associated gradient flow, examining how rotationally symmetric initial data can lead to global existence and flow convergence, independent of initial energy conditions. Gain insights into this specialized area of geometric analysis presented as part of the 2025 ESI mathematics series.