nLab Damien Calaque

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Selected writings

On tensor categories:

• Damien Calaque, Pavel Etingof, Lectures on tensor categories, IRMA Lectures in Mathematics and Theoretical Physics 12, 1-38 (2008) (arXiv:math/0401246)

On the Duflo isomorphism:

• Damien Calaque, Carlo A. Rossi, Lectures on Duflo isomorphisms in Lie algebra and complex geometry, European Math. Soc. (2011) [doi:10.4171/096, pdf]

On mapping stacks and TFT:

• Damien Calaque, Lagrangian structures on mapping stacks and semi-classical TFTs, 2013, arXiv:1306.3235.

On derived symplectic geometry (shifted symplectic structures):

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

  pdf - see also these notes

• 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

On preprojective algebras and Calabi-Yau structures

• Tristan Bozec, Damien Calaque, Sarah Scherotzke, Calabi-Yau structures for multiplicative preprojective algebras, J. Noncommut. Geom. 17 3 (2023) 783-810 [arXiv:2102.12336]

Review of formal moduli problems via $L_\infty$-algebras:

• Damien Calaque, Julien Grivaux: Formal moduli problems and formal derived stacks, in Derived Algebraic Geometry, Panoramas & Synthèses 55, AMS (2021) 85-145 [arXiv:1802.09556, pdf, ISBN:978-2-85629-938-8]

Discussion of the AKSZ sigma-model as an extended functorial field theories via derived algebraic geometry:

• Damien Calaque, Rune Haugseng, Claudia Scheimbauer: The AKSZ Construction in Derived Algebraic Geometry as an Extended Topological Field Theory, Memoirs of the American Mathematical Society 308 1555 (2025) [arXiv:2108.02473, doi:10.1090/memo/1555]

Review of shifted symplectic structures:

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

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