nLab shifted symplectic structure

Idea

The derived geometry-version of symplectic geometry.

Related concepts

• symplectic structures

• derived algebraic geometry

• AKSZ sigma-model

• BV-BRST formalism

References

• Tony Pantev, Bertrand Toen, Michel Vaquie, Gabriele Vezzosi, Shifted symplectic structures, Publ. Math. IHES 117:1 (2013) 271–328 arXiv:1111.3209

• Damien Calaque, Lagrangian structures on mapping stacks and semi-classical TFTs, arXiv:1306.3235.

• Damien Calaque, Three lectures on derived symplectic geometry and topological field theories, 2014,

  pdf - see also these notes

• Pavel Safronov, Quasi-Hamiltonian reduction via classical Chern–Simons theory, arXiv:1311.6429

• James Wallbridge, Derived smooth stacks and prequantum categories, arxiv/1610.00441

• Xiaojun Chen, Farkhod Eshmatov, Calabi-Yau algebras and the shifted noncommutative symplectic structure, arXiv:1802.07423

Darboux theorem:

• Chris Brav, Vittoria Bussi, Dominic Joyce, A Darboux theorem for derived schemes with shifted symplectic structure, 2013, arXiv:1305.6302.

• Oren Ben-Bassat, Christopher Brav, Vittoria Bussi, Dominic Joyce, A ‘Darboux Theorem’ for shifted symplectic structures on derived Artin stacks, with applications, arXiv:1312.0090

• Pavel Safronov, Dominic Joyce, A Lagrangian Neighbourhood Theorem for shifted symplectic derived schemes, arXiv:1506.04024

Shifted Poisson structures

• Damien Calaque, Tony Pantev, Bertrand Toen, Michel Vaquie, Gabriele Vezzosi, Shifted Poisson structures and deformation quantization, Journal of topology 10.2 (2017) 483–584 arXiv:1506.03699

• Valerio Melani, Poisson bivectors and Poisson brackets on affine derived stacks, arXiv:1409.1863

• J. P. Pridham, Shifted Poisson and symplectic structures on derived N-stacks, arXiv:1504.01940

• J. P. Pridham, Shifted bisymplectic and double Poisson structures on noncommutative derived prestacks, arXiv:2008.11698

• J. P. Pridham, Shifted symplectic structures on derived analytic moduli of l-adic local systems and Galois representations, arXiv:2205.02292

• Pavel Safronov, Poisson reduction as a coisotropic intersection, arXiv:1509.08081

Review:

• Damien Calaque, Derived symplectic geometry, Encyclopedia of Mathematical Physics 2nd ed [arXiv:2308.04210]