Research

Alessio Figalli specializes in the wide-ranging fields of Calculus of Variations and Partial Differential Equations, focusing especially on optimal transport, functional and geometric inequalities, elliptic partial differential equations, and free boundary problems. His work also extends into other areas within both pure and applied mathematics. For more details,   click here

For a list of Selected Papers,   click here

For a list of all his publications, you can follow the links below:

Published/Accepted Papers       Submitted Papers      Surveys and lecture notes      Books

Research areas

For a list of publications divided into research areas, you can click on the links below.

• General optimal transport theory
• Regularity of optimal maps and Monge-Ampère equations
• Optimal transport and Riemannian geometry
• Free boundary problems
• Evolution equations and gradient flows
• Functional and geometric inequalities
• Non-local energies and elliptic operators
• Calculus of Variations
• Elliptic PDEs
• Transport equations
• Sets of finite perimeter and geometric measure theory
• Dynamical systems, weak KAM, and sympletic geometry
• Stochastic analysis and random matrices
• Applied Mathematics