FJ-LMI Seminar

Seminar information archive ~04/30Next seminarFuture seminars 05/01~

Organizer(s) Toshiyuki Kobayashi, Michael Pevzner

2025/04/17

15:00-15:45   Room #056 (Graduate School of Math. Sci. Bldg.)
Pierre SCHAPIRA (IMJ - Sorbonne University)
Sheaves for spacetime (英語)
[ Abstract ]
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 notion of a causal pre-order. 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 neighborhood 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.
[ Reference URL ]
https://fj-lmi.cnrs.fr/wp-content/uploads/2025/02/Tokyo25Sem.pdf