AbstractIn the modular (char p) representation theory of algebraic reductive groups, the Frobenius twist is a great self-symmetry of the category of representations. Geometrically this self-symmetry is related to the embedding of the affine grassmannian, which is the based loop space of the reductive group, into itself as based loops that repeat themselves for p times. I'll explain an interpret...
Abstract:Whether the 3D incompressible Euler equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In this talk, we will present a new exciting result with Dr. Jiajie Chen in which we prove finite time blowup of the 2D Boussinesq and 3D Euler equations with smooth initial data and boundary. There are several essentia...