Luca Rizzi

Luca Rizzi is a Full Professor at International School for Advanced Studies (SISSA) in Trieste, Italy, where he serves as the Coordinator of the PhD program in Mathematical Analysis, Modeling, and Applications and Principal Investigator of the ERC Starting Grant Project GEOSUB (2022-2026). His research focuses on Geometric Control Theory and Sub-Riemannian Geometry, with significant contributions to the geometric analysis of spaces with non-holonomic constraints.

His research interests include:

• Geometric Control Theory
• Sub-Riemannian Geometry
• Optimal Control Problems
• Geometric Analysis

Rizzi leads the GEOSUB project developing geometric and functional interpolation inequalities for sub-Riemannian manifolds, with implications for geometric analysis on non-smooth spaces, hypoelliptic operators, and geometric measure theory. His work bridges theoretical mathematics with applications in control theory and geometric structures.

His scientific recognition includes:

• ERC Starting Grant for Project GEOSUB (2022-2026)

Rizzi mentors PhD students Dario Sterzi and Daniele Tiberio, and supervises postdocs Samuel Borza, Giorgio Stefani, and Ye Zhang. He organizes the Geometric Structures seminar at SISSA and manages a sub-Riemannian community mailing list with over 200 subscribers. He has organized numerous conferences including the Workshop on Geometric Variational Problems in Sub-Riemannian Geometry (2025), Riemann 200: Mathematics and Physics (2026), and the XXXV Convegno Nazionale di Calcolo delle Variazioni (2026).

As a member of the editorial board of the Journal of Dynamical and Control Systems, Rizzi actively contributes to advancing research in his field through academic service and international collaboration.