Prof. Maria Colombo, head of the Chair of Mathematical Analysis, Calculus of Variations and PDEs (AMCV), received the grant for her project TENSE, with title "Irregular solutions of the Transport, Euler and Navier-Stokes Equations".
Prof. Nicolas Boumal, head of the Chair of Countinuous Optimization (OPTIM), received the grant for his project GEOSYM, with title "Harnessing Geometry and Symmetry in Optimization for Data Science".
The celebrated Euler and Navier-Stokes equations of fluid dynamics model the motion of particles in an inviscid and in a viscous fluid, respectively. Their mathematical understanding poses formidable challenges, mainly stemming from the presence of irregular solutions. The behavior of these irregular solutions has, in turn, fascinating and still not fully understood connections with physical problems involving turbulent phenomena. In this area, some recent breakthrough results constitute a step forward: for instance, the proof of the Onsager conjecture in the framework of the Kolmogorov theory of turbulence and certain quantitative bounds on mixing rates.
The goal of Maria Colombo and of her research team is to provide new insight on the theoretical understanding of irregular solutions, answer fundamental questions about (non)-uniqueness of solutions and typicality of nonsmooth behaviors.
Continuous optimization is a cornerstone of technology: we use it to transform vast amounts of data into actionable information, be it by solving inverse problems in imaging, performing statistical estimation in signal processing or training neural networks in machine learning. To realize the full potential of these computational tools, we need to push our understanding of the limits and opportunities of optimization beyond the classical mathematical framework (convexity).
With the project GEOSYM, the goal of Nicolas Boumal and his team is to harness other mathematical structures that are ubiquitous in applications, namely, geometry and symmetry, to tackle non-convex optimization reliably.
The ERC Starting Grants are given each year to researchers of any nationality and in any field of research with 2-7 years of research experience after the completion of their PhD and who show a promising scientific track record, and offer an excellent research proposal. Each Starting Grant can be up to €1.5 million given over a period of five years.
Due to the non-association of Switzerland to Horizon Europe, their projects will be financed by Switzerland (SERI).