Explore advanced mathematical concepts in this 22-minute research presentation from the ESI's Thematic Programme on "Infinite-dimensional Geometry: Theory and Applications." Delve into groundbreaking research on minimal hypersurfaces and their applications in discrete geometry, building upon doctoral thesis findings to expand understanding of minimal submanifolds. Learn about the properties of harmonic hypersurfaces through biharmonic submanifolds, examining their characterization in Euclidean spaces, complex Euclidean spaces, and Sasakian space forms. Discover how harmonic and biharmonic maps play crucial roles in discrete geometry, particularly in shape analysis and tracking, drawing from six published works in international journals.