We are thrilled to announce a monumental achievement in the field of mathematics by Elia Bruè, a distinguished member of our Department of Decision Sciences at Bocconi University. Alongside his esteemed colleagues, Aaron Naber from Northwestern University and Daniele Semola from the Swiss Federal Polytechnic in Zurich, Bruè has successfully disproved a long-standing conjecture in Riemannian Geometry, originally proposed by the renowned mathematician John Milnor in 1968.

Milnor's conjecture posited that a manifold (a multi-dimensional geometric shape) with nonnegative Ricci curvature (a measure of how the shape bends) could not possess infinitely many holes. In a groundbreaking development, Bruè and his colleagues have constructed a seven-dimensional manifold that challenges this assumption. Their counterexample demonstrates that it is indeed possible for such a shape to have nonnegative Ricci curvature while also having an infinitely complex hole structure, as indicated by a non-finitely generated fundamental group.

This revelation, published in the prestigious scientific journal Quanta, marks a significant advancement in our understanding of geometric shapes. The implications of this discovery extend beyond theoretical mathematics, potentially influencing future studies in geometry and related fields. It raises intriguing new questions about the behavior of manifolds in different dimensions and under varying geometric constraints, opening avenues for further research and exploration.

Elia Bruè's achievement not only brings pride to our institution but also places us at the forefront of contemporary mathematical research. We extend our heartfelt congratulations to Elia Bruè and his collaborators for their remarkable accomplishment.