Mattia Magnabosco

Post Doctorial Research Associate

Education

PhD in Mathematics, Bonn International Graduate School of Mathematics, Bonn Germany - 2023

Diploma in Mathematics, Scuola Normale Superiore, Pisa Italy - 2021 

MSc in Mathematics, University of Pisa - 2020

Bachelor’s degree in Mathematics, University of Pisa - 2018

Research Group

Differential Geometry

Research Area

Metric Geometry, Differential Geometry, Geometric Analysis

Bio

Research Interests

I work in differential and metric geometry, with particular interests in geometric analysis, geometric measure theory, and topology. A central theme of my research is understanding how lower curvature bounds constrain the geometric, analytic, and topological structure of spaces, both in the classical smooth setting and in the broader framework of metric measure spaces.

I am particularly interested in the structure of spaces with synthetic lower curvature bounds and in the development of geometric and analytic tools for studying non-smooth spaces. My research includes questions concerning the rectifiability and structure of spaces satisfying curvature-dimension bounds, as well as the geometry of non-Riemannian settings such as sub-Riemannian and sub-Finsler spaces. More recently, I have also become interested in global questions connecting lower curvature bounds with the topology and large-scale geometry of Riemannian manifolds and metric measure spaces. More broadly, my work draws on ideas from optimal transport, geometric measure theory, nonlinear analysis, and calculus of variations.

Selected Publications

• New Topological Restrictions For Spaces With Nonnegative Ricci Curvature, with Alessandro Cucinotta and Daniele Semola, preprint, 2026.
• On perimeter minimizing sets in manifolds with quadratic volume growth, with Alessandro Cucinotta, Journal für die reine und angewandte Mathematik, 2026.
• Gradient flows of (K,N)-convex functions with negative N, with Lorenzo Dello Schiavo and Chiara Rigoni, Calculus of Variations and Partial Differential Equations, 2026.
• The curvature exponent of sub-Finsler Heisenberg groups, with Samuel Borza, Tommaso Rossi and Kenshiro Tashiro, SIAM Journal on Mathematical Analysis, 2025.
• Almost-Riemannian manifolds do not satisfy the curvature-dimension condition, with Tommaso Rossi, Calculus of Variations and Partial Differential Equations, 2023.