Alessio Figalli studies optimal transport, a field of math that ranges from the movements of clouds to the workings of chatbots. By Siobhan Roberts The words “optimal” and “optimize” derive from the ...

We study Monge's optimal transportation problem, where the cost is given by an optimal control cost. We prove the existence and uniqueness of an optimal map under certain regularity conditions on the ...

Joint research led by Sosuke Ito of the University of Tokyo has shown that nonequilibrium thermodynamics, a branch of physics that deals with constantly changing systems, explains why optimal ...