What I understood about the principle of least action and its geometric aspects Bruno Levy Institut National de Recherche en Informatique Automatique (INRIA) - Lorraine The principle of least action is an elegant mathematical model for a wide range of phenomena in physics. From a very limited number of concepts, it mathematically implies conservation laws (energy, momentum, rotational momentum), Newton laws (F=ma), and is the starting point of Euler's mathematical modeling of fluids. After a brief introduction, I will give an overview of some of its connections with different domains, including mathematics (optimal transport theory) [Brenier], [Benamou and Brenier], computational geometry (power diagrams) [Aurenhammer Hoffman Aranov], [Alexandrov], [Merigot], [L] and new methods for computational physics [Merigot], [Desbrun]. I will also present some efficients algorithms to solve the Monge-Ampère equation, a fundamental building block for this family of numerical methods [Jordan, Kinderlehrer, Otto], [Merigot] that may also have applications in geometry processing / shape analysis / shape correspondence.