Shifted Symplectic Geometry by Examples

2025/10/06 by Damien Calaque, Calaque, Damien, Stefano Ronchi +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Symplectic Geometry (math.SG) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2510.04625

openalex publication_date 2025/10/06 · openalex created_date 2025/10/09 · openalex updated_date 2026/07/28

Abstract

These notes are intended to be an introduction to shifted symplectic geometry, targeted to Poisson geometers with a serious background in homological algebra. They are extracted from a mini-course given by the first author at the Poisson 2024 summer school that took place at the Accademia Pontaniana in Napoli.

Citations

• Lecture notes on the symplectic geometry of graded manifolds and higher Lie groupoids
• Introduction to moduli spaces and Dirac geometry
• The Moore-Tachikawa conjecture via shifted symplectic geometry
• Shifted cotangent bundles, symplectic groupoids and deformation to the normal cone
• Shifted symplectic higher Lie groupoids and classifying spaces
• The AKSZ Construction in Derived Algebraic Geometry as an Extended Topological Field Theory
• Shifted symplectic Lie algebroids
• Derived Algebraic Geometry and Deformation Quantization
• Quasi-Hamiltonian reduction via classical Chern–Simons theory
• A 'Darboux theorem' for derived schemes with shifted symplectic\n structure
• Shifted Symplectic Structures
• Representations up to homotopy of Lie algebroids
• Symmetric obstruction theories and Hilbert schemes of points on threefolds
• Homotopical Algebraic Geometry II: geometric stacks and applications
• Momentum Maps and Morita Equivalence
• Topological and Smooth Stacks
• Derived Quot schemes
• Lie Group Valued Moment Maps
• Symplectic Geometry

Related

• Lectures on shifted Poisson geometry
• Symplectic Geometry, Poisson Geometry, and Beyond
• Symplectic Geometry
• Symplectic and Poisson derived geometry and deformation quantization
• Shifted symplectic structure on Poisson Lie algebroid and generalized complex geometry