Speaker
Description
We shall study the Cauchy problem on globally hyperbolic manifolds with the only tools of microlocal sheaf theory and the precise Cauchy-Kowalevski theorem.
A causal manifold is a manifold $M$ endowed with a closed convex proper cone $\lambda\subset T^*M$. On such a manifold, one defines the $\lambda$-topology and the associated notions of a causal pre-order and a causal path. One introduces the notion of a G-causal manifold, those for which there exists a time function. On a G-manifold, sheaves satisfying a suitable condition on their micro-support and defined on a neigborhood of a Cauchy hypersurface extend to the whole space. When the sheaf is the complex of hyperfunction solutions of a hyperbolic $\mathcal{D}$-module, this proves that the Cauchy problem is globally well-posed.
We will also describe a "shifted spacetime" associated with the quantization of an Hamiltonian isotopy.
This talk is partly based on papers in collaboration with Benoît Jubin, Stéphane Guillermou and Masaki Kashiwara.
