Research summary
The optimal transportation theory aims to answer the question of how to transfer mass from one place to another as efficiently as possible and at the lowest cost. Dr. Robert McCann, Canada Research Chair in Mathematics, Economics and Physics, is developing new mathematical tools from optimal transportation and variational calculus to analyze key models from physics, geometry and economics.
He and his research team are working to understand the structure or absence of singularities in optimal maps between given pairs of mass distributions. They are also analyzing how patterns form in nonlinear, nonlocal models for various physical, biological and economic processes. In addition, they are recasting Einstein’s theory of gravity into a non-smooth framework. This will shed light on the limiting geometry of sequences of space-times and provide a new setting for exploring possible singularities among other phenomena.