Research

Prof. Alessio Figalli works in the broad areas of Calculus of Variations and Partial Differential Equations, with particular emphasis on optimal transportation, Monge-Ampère equations, functional and geometric inequalities, elliptic PDEs of local and non-local type, free boundary problems, Hamilton-Jacobi equations, transport equations with rough vector-fields, and random matrix theory. For a description,   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
• Evolution equations and gradient flows
• Functional and geometric inequalities
• Transport equations
• Free boundary problems
• Non-local energies and elliptic operators
• Calculus of Variations
• Elliptic PDEs
• Sets of finite perimeter and geometric mesure theory
• Dynamical systems, weak KAM, and sympletic geometry
• Stochastic analysis and random matrices