**Abstract:**

In this talk
we discuss an algorithm to overcome the curse of
dimensionality, in possibly non-convex/time/state-dependent Hamilton-Jacobi
partial differential equations. They may arise from
optimal control and differential game problems, and are
generally difficult to solve numerically in high
dimensions. A major contribution of our works is to
consider an optimization problem over a single vector of
the same dimension as the dimension of the HJ PDE
instead. To do so, we consider the new approach
using Hopf-type formulas. The sub-problems are now
independent and they can be implemented in an
embarrassingly parallel fashion. That is ideal for
perfect scaling in parallel computing.The algorithm is
proposed to overcome the curse of dimensionality when
solving high dimensional HJ PDE. Our method is expected to
have application in control theory, differential game
problems, and elsewhere. This approach can be
extended to the computational of a hamilton-Jacobi
equation in the Wasserstein space, and is expected to have
applications in mean field control problems, optimal
transport and mean field games.