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...
Abstract: We review recent progress in 3d-3d correspondence, with a focus on new topological invariants and on interesting topological quantum field theories (TQFTs). In particular, we discuss how this line of development can help to bridge topology and quantum topology