Research Fellows Directory
Professor Andre Neves
Imperial College London
A natural question in Nature is to know what is the optimal configuration of some object. In Geometry, shapes that are in some equilibrium configuration are called minimal surfaces and they are ubiquitous in Science, serving to model soap films, black holes in General Relativity, or tensile structures in architecture.
Minimal surfaces come in two types: those for which small perturbations increase their area (stable equilibrium) and those which admit perturbations that decrease their area (unstable equilibrium). The first type has been heavily studied in Geometry because they can be obtained by minimizing area among all surfaces that cannot be squashed to a point and their applications to Geometry have been immense in the last 40 years. My current research is focused on unstable minimal surfaces because very little is known and their properties are tied with questions in topology and analysis.