Microlocal analysis and beyond

TL;DR

This paper reviews the evolution of microlocal analysis from its origins in the 1970s to its reformulation using sheaf theory in the 1980s, highlighting its applications across different mathematical fields.

Contribution

It introduces a sheaf-theoretic reformulation of microlocal analysis and demonstrates its applications in PDEs and symplectic topology.

Findings

Sheaf theory provides a new framework for microlocal analysis.

Applications include advances in linear PDEs and symplectic topology.

The reformulation broadens the scope of microlocal techniques.

Abstract

We shall explain how the idea of microlocal analysis of the seventies has been reformulated in the framework of sheaf theory in the eighties and then applied to various branches of mathematics, such as linear partial differential equations or symplectic topology.