Magdalena Toda
Texas Tech University & National Science Foundation, USA

Functionals involving surface curvature are extensively used as models for elastic phenomena. Their critical points are frequently representative of physically relevant structures such as biomembranes or material interfaces. This talk will combine a variational characterization of curvature functionals and their critical surfaces, with computational models of elastic surfaces.

Examples will be presented, from minimal surfaces to generalizations of Willmore and Helfrich surfaces. Applications of elastic surface theory to biomembranes and protein models will be discussed briefly, in the context of geometric PDE, calculus of variations, differential geometry and Lie groups. If time permits, some recent results in terms of stability for $p$-Willmore surfaces will be presented. Likewise, some analysis for surfaces with boundaries (fixed boundary or/and fixed boundary) may be discussed.

Some computational models will be presented briefly, based on recent results and models created in collaboration with Alvaro Pampano, Hung Tran, Anthony Gruber, and Eugenio Aulisa.