This work broadens previous results on harmonic measure by proving that, for planar Reifenberg flat domains and uniformly elliptic operators with Lipschitz coefficients, the Hausdorff dimension of the associated elliptic measure is at most one.

In this talk, Roderic Guigó argues that the success of computational biology is not just about big data—it’s about the symbolic nature of molecular information, making it uniquely suited for computational and mathematical approaches.

The results, published in Calculus of Variations and Partial Differential Equations, lay the foundation for a unified theory of convergences in nonlocal models, bridging operator and variational perspectives and opening the door to applications in mathematics, physics, and engineering.

This also enabled them to provide a second (variational) proof of the H-compactness theorem, through of Γ-convergence.

They introduced new ideas to overcome the limitations of traditional localization techniques, proved H-compactness for a broad class of operators, and established the equivalence between H-convergence and Γ-convergence in the symmetric case.

Their collaboration extended the classical theories of H- and Γ-convergence to the nonlocal setting, focusing on linear operators in fractional divergence form.

Thanks to this initiative, researchers Maicol Caponi (Università degli Studi dell’Aquila), Alessandro Carbotti (Università del Salento), and Alberto Maione @crmatematica.bsky.social were able to work intensively at CRM, which allowed them to make significant progress in calculus of variations.

This achievement is a clear example of the impact of the International Programme for Research in Groups (IP4RG) at the Centre de Recerca Matemàtica @crmatematica.bsky.social .

Investigate automorphisms of the double affine Hecke algebra (DAHA) of type Č₁C₁, focusing on symmetries that act in a relatively simple way on generators and parameters, and their impact on the basic representation as well as on symmetric and non-symmetric Askey–Wilson polynomials and functions.

Tom Koornwinder (University of Amsterdam) and Marta Mazzocco @icreacommunity.bsky.social - @upc.edu - @crmatematica.bsky.social present a work published in Indagationes Mathematicae.

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provide new insights into the stability and evolution of viral infections, a promising field for the design of antiviral strategies based on defective genomes.

Oriol Llopis-Almela @crmatematica.bsky.social J. Tomás Lázaro @crmatematica.bsky.social – @upc.edu , Santiago F. Elena @uv.es - @sfiscience.bsky.social and Josep Sardanyés @crmatematica.bsky.social

Join us at the CRM for a workshop that brings together leading researchers working at the intersection of partial differential equations, dynamical systems, and probability, to explore how these tools illuminate the theory and practice of modern machine learning.

Machine learning is transforming science and technology—but its mathematical foundations remain a rich and evolving frontier.