Luis Caffarelli


"My main area of research centers on the properties of solutions to Partial Differential Equation. Partial Differential equations are the most common way to give a mathematical formulation to the evolution of continuous phenomena: water waves, the deformation of an elastic body, the propagation of heat or aspecies, the formation of opinions or a price. It is based on the idea the configuration in the large (the shape of anelastic body put to rest on a surface) is the result of the "infinitesimal interaction of each particle with those surrounding it." It is often the bases for numerical simulation and prediction. Of my own work, some of the research I like the best consists of the understanding of 'phase transition models' like a solid liquid interphase or the shape of a flame, the properties of flows, and the optimization of shapes or strategies."