ERC Starting Grants for Alessandro Carlotto and Joaquim Serra
Alessandro Carlotto and Joaquim Serra are two of twelve talented young researchers that receive a Starting Grant from the European Research Council (ERC).
Alessandro Carlotto works in differential geometry, which is the area of mathematics that concerns the study of shapes through the notion of curvature. His project is built around a network of problems that are partly "pure" in nature and partly stem from general relativity, Einstein's theory describing gravity in terms of the curvature of space-time. A key aspect of Carlotto's investigation is the interplay between these two worlds. For instance, the study of minimal surfaces (fascinating geometric objects that behave like a soap bubble) and of Plateau's problem has been a driving force in 20th century mathematics and is something we now understand quite well. The intrinsic counterpart of the story, however, which has to do with Riemannian filling problems and certain notions of quasi-local mass of isolated gravitating systems, remains extremely elusive. The goal of the project is to shed light on some of these mysteries.
In his research, Joaquim Serra examines partial differential equations. These mathematical equations describe many natural phenomena like waves, heat, electric and gravitational potentials, fluid dynamics and quantum mechanics. In his ERC project, he will deal with classical models for interfaces, or separating surfaces. Their behaviour can be imagined as similar to two unmixable liquids of the same density moving in a "lava lamp" and thus forming decorative patterns. To describe them, certain quite delicate equations are used. They often have many solutions with exotic structures, but only few of them are stable enough to be observable in nature. Serra's objective is to understand the properties of these observable solutions. In doing so, he will try to suitably translate the knowledge gained in recent years from studying simpler models in order to elucidate new properties of these delicate equations.
Twelve ERC Starting Grants for ETH Zurich (ETH News, 3.9.2020)