Mathematician Andrea Merlo to lead the ERC Starting Grant DARTS project

BCAM will host this cutting-edge research starting January 1, 2027. Funded by the European Research Council, the project aims to solve fundamental questions in Geometric Measure Theory and open new horizons in the analysis of partial differential equations.

BCAM reinforces its position in the international elite of fundamental mathematics with the award of a Starting Grant (ERC StG 2026) granted by the European Research Council to Ikerbasque researcher at BCAM Andrea Merlo. Endowed with funding of €1,450,073 and a duration of 5 years (60 months), the DARTS project (“Densities and regularity of tangents in metric measure spaces”) will formally kick off on January 1, 2027, at the BCAM facilities in Bilbao.

The prestigious ERC Starting Grants represent the most coveted European recognition for early-career researchers with a promising track record and proven capacity to lead disruptive frontier science. Through DARTS, Andrea Merlo will address open problems that have persisted for over three decades in Geometric Measure Theory (GMT), formulating a unified framework connecting the geometry of non-Euclidean metric spaces, quantitative differentiability, and boundary value problems in partial differential equations (PDEs).

A mathematical bridge between metric geometry and differential equations

For decades, one of the major obstacles in geometric analysis has been the absence of a unifying principle in metric measure spaces that analytically links densities to the structure of their tangent spaces, as well as the lack of criteria transforming locally modeled tangents on Carnot groups into global geometric regularity. The DARTS project is structured around three scientific objectives of maximum impact:

• Resolution of the density problem in metric spaces: Proving that the existence of positive and finite densities forces almost everywhere that tangent spaces (in the Gromov-Hausdorff sense) are uniform metric groups equipped with their Haar measure. This will establish a metric analog of the famous Preiss theorem and solve the historical 1-density problem.
• Proof of the WALA conjecture and uniform rectifiability: Establishing that the quantitative affine approximability of Lipschitz functions (WALA property) implies uniform rectifiability both in the Euclidean space $\mathbb{R}^n$ and in metric spaces, providing decisive tools to answer the regularity problem in elliptic operators formulated over 30 years ago.
• Metric extension of the Marstrand-Mattila rectifiability criterion: Precisely determining when tangents modeled on a Carnot group force bi-Lipschitz rectifiability with respect to those groups, solving Besicovitch-type projection theorems and Reifenberg flat disk theorems with Carnot models.

Beyond its immense value in pure mathematics, these solutions will allow a rigorous understanding of the solvability of boundary value problems in degenerate kinetic equations, such as Kolmogorov–Fokker–Planck operators on rough and time-dependent domains, connecting abstract geometry with real physical problems.

"The DARTS project aims to decipher how the analytical information of density intrinsically shapes the geometry of rough and complex spaces. Understanding how the existence of density implies the existence of a local algebraic structure compatible with the metric structure will be of huge relevance both theoretically and in terms of applications. With DARTS, we will not only research questions regarding the geometry of metric spaces, but also export them to the field of partial differential equations. Establishing this research program at BCAM from January 2027 represents an exceptional opportunity to build a leading team at the center."

— Dr. Andrea Merlo, Principal Investigator of DARTS

About Andrea Merlo: a career at the forefront of European mathematics

Born in Valdobbiadene (Italy) in 1992, Dr. Andrea Merlo earned his PhD with cum Laude honors in Mathematics in 2020 at the prestigious Scuola Normale Superiore in Pisa, defending his thesis "Geometry of 1-codimensional measures in Heisenberg groups" under the supervision of Giovanni Alberti and Roberto Monti. During his doctorate, he independently conceived and solved the extension of Preiss's theorem to the Heisenberg group, published as a single author in Inventiones Mathematicae (2022), one of the world's most impactful mathematics journals.

His outstanding scientific career has been recognized with prestigious awards in Italy, such as the INDAM–UMI–SIMAI Prize, the Gioacchino Iapichino Prize, and the Guido Stampacchia Prize. Before establishing himself as an Ikerbasque Research Fellow in the Basque Country, he completed postdoctoral stages at Université Paris-Saclay (France, with Guy David), Université de Fribourg (Switzerland, with Enrico Le Donne), and held a prestigious individual Marie Skłodowska-Curie European fellowship (MSCA Postdoctoral Fellowship). He has over 20 publications and preprints in top-tier journals such as Inventiones Mathematicae, ARMA, Memoirs AMS, Proceedings of the London Mathematical Society, Analysis & PDE, Journal of Functional Analysis, and Calculus of Variations and PDEs.

Talent attraction and building a team of excellence at BCAM

Andrea Merlo joins BCAM in the position of Ikerbasque Associate Professor. The ERC Starting Grant will allow Andrea Merlo to establish a high-performance international research team at BCAM comprising four postdoctoral researchers and one PhD student, selected through competitive international calls. In addition to pure research work, the project includes an intense dissemination agenda featuring an International School on Geometric Measure Theory in its first year, two large-scale international conferences in Bilbao (years 3 and 5), and several thematic workshops bringing together top world specialists in metric analysis and PDEs.