Research

OPTIMAL TRANSPORT (OT)

Optimal Transport studies the most efficient ways to move mass, linking probability, analysis, and geometry. 

At MathUB, research explores both the classical Monge–Kantorovich theory and modern regularized formulations. Optimal Transport provides a geometric framework for gradient flows, entropy minimization, and measure evolution problems. Our group contributes to the rigorous development of these structures and their applications in analysis. 

PARTIAL DIFFERENTIAL EQUATIONS (PDEs)  

PDE research at MathUB focuses on nonlinear and geometric equations arising in analysis and geometry. 

The group investigates diffusion, transport, and curvature-driven flows through variational and metric tools. Work by Bruè, De Rosa, and collaborators explores regularity, evolution equations, and geometric constraints. Connections with optimal transport and gradient flows are a central feature of this line of research. 

METRIC ANALYSIS

Metric Analysis extends classical calculus to spaces lacking smooth structure, using metric and variational techniques.

It plays a central role in the analysis of gradient flows, optimal transport, and PDEs on non-smooth spaces. Research by Savaré, Bruè, and Lavenant builds bridges between geometry, probability, and analysis.

Our work shapes modern understanding of curvature, regularity, and functional inequalities on metric measure spaces. 

CALCULUS OF VARIATIONS

The Calculus of Variations investigates the existence and regularity of minimizers in geometric and physical problems. MathUB’s work connects geometric measure theory, minimal surfaces, and free-boundary variational problems. Pigati and De Rosa contribute key results in min–max theory and curvature-driven minimization.

These studies reveal deep links between variational principles, topology, and geometric PDEs.