For initial datum of finite kinetic energy Leray has proven in 1934 that there exists at least one global in time finite energy weak solution of the 3D Navier-Stokes equations. In this talk, I will discuss very recent joint work with Vlad Vicol in which we prove that weak solutions of the 3D Navier-Stokes equations are not unique in the class of weak solutions with finite kinetic energy.
Lattices are periodic arrangements of points in space that have attracted the attention of mathematicians for over two centuries. They have recently become an object of even greater interest due to their remarkable applications in cryptography. In this talk we will survey some of this progress and describe the somewhat mysterious role that quantum computing plays in the area.