Symplectic and Poisson derived geometry and deformation quantization

TL;DR

This paper reviews recent advances in the symplectic and Poisson geometry of derived moduli spaces and discusses their applications to deformation quantization.

Contribution

It provides a comprehensive overview of recent results and ongoing research in the symplectic and Poisson derived geometry and their role in deformation quantization.

Findings

Summarizes recent developments in derived symplectic and Poisson geometry.

Highlights applications to deformation quantization of derived moduli spaces.

Identifies open problems and directions for future research.

Abstract

We review recent results and ongoing investigations of the symplectic and Poisson geometry of derived moduli spaces, and describe applications to deformation quantization of such spaces.