| Abstract |
Symplectic geometry is the study of geometric problems initially arising from physical dynamics including classical and quantum mechanics, optics, and thermodynamics. Mathematically speaking, symplectic geometry concerns about geometric properties that are invariant under symplectic transformations (transformations that preserve the symplectic differential structure) and one often regards the field as a branch of differential geometry. Recently, there is an increasing interest in studying the properties beyond its differential structure which we call C^0 symplectic geometry. The first part of this talk will be an introduction of symplectic geometry and its C^0 developments. In the second part, I will discuss a hierarchy of coisotropic rigidities that generalizes the classical C^0 rigidity of symplectic transformations. Thirdly, I will apply microlocal sheaf theory to give a new definition of coisotropic set and show that this new notion improves the above mentioned hierarchy of rigidities. The last part is based on a joint work in preparation with Yuichi Ike and Tomohiro Asano. |
