Damien Calaque

Damien Calaque

Professor at IMAG (Univ Montpellier)

PI of ERC Project Derived Symplectic Geometry and Application

Email: damien.calaque[at]umontpellier.fr


Work in progress


[5] Shifted cotangent bundles, symplectic groupoids and deformation to the normal cone (with Pavel Safronov),
Freely available at arXiv:2407.08622
[4] Associators from an operadic point of view (with Victor Roca i Lucio),
Freely available at arXiv:2402.05539
[3] Wild orbits and generalised singularity modules: stratifications and quantisation (with Giovanni Felder, Gabriele Rembado and Richard Wentworth),
Freely available at arXiv:2402.03278
[2] Lie algebroids are curved Lie algebras (with Ricardo Campos and Joost Nuiten),
Freely available at arXiv:2103.10728
[1] An operadic approach to cyclotomic associators (with Martin Gonzalez),
Freely available at arXiv:2004.00572


[1] Lectures on Duflo isomorphisms in Lie algebra and complex geometry (with Carlo A. Rossi),
EMS Series of Lectures in Mathematics 14 (2011), EMS Publishing House
Preliminary version freely available on my lecture notes page


[37] The AKSZ construction in derived algebraic geometry as an extended topological field theory (with Rune Haugseng and Claudia Scheimbauer),
To appear in Memoirs of the AMS.
Freely available at arXiv:2108.02473
[36] Relative critical loci and quiver moduli (with Tristan Bozec and Sarah Scherotzke),
Annales Scientifiques de l'ENS 57 (2024), no. 2, 553-614.
Freely available at arXiv:2006.01069
[35] Ellipsitomic associators (with Martin Gonzalez),
Mémoires de la SMF 179 (2023), 96 pages.
Freely available at arXiv:2004.07271
[34] Calabi-Yau structures on (quasi-)bisymplectic algebras (with Tristan Bozec and Sarah Scherotzke),
Forum of Mathematics, Sigma 11 (2023), article 87, 32 pages.
Freely available at arXiv:2203.14382
[33] Calabi-Yau structures for multiplicative preprojective algebras (with Tristan Bozec and Sarah Scherotzke),
Journal of Noncommutative Geometry 17 (2023), no. 3, 783-810.
Freely available at arXiv:2102.12336
[32] Shifted symplectic reduction of derived critical loci (with Mathieu Anel),
Advances in Theoretical and Mathematical Physics 26 (2022), no. 6, 1543-1583.
Freely available at arXiv:2106.06625
[31] Moduli problems for operadic algebras (with Ricardo Campos and Joost Nuiten),
Journal of the LMS 106 (2022), no. 4, 3450-3544.
Freely available at arXiv:1912.13495, or on the publisher's site
[30] Formal moduli problems and formal derived stacks (with Julien Grivaux),
In Derived Algebraic Geometry (B. Toën & M. Vaquié Eds.), Panoramas et Synthèses 55 (2021), 85-146.
Freely available at arXiv:1802.09556
[29] Derived stacks in symplectic geometry,
In New Spaces in Physics: Formal and Conceptual Reflections (M. Anel & G. Catren Eds.), Cambridge University Press (2021), 155-201.
Freely available at arXiv:1802.09643
[28] On the universal ellipsitomic KZB connection (with Martin Gonzalez),
Selecta Mathematica 26 (2020), no. 5, article 73, 59 pages.
Freely available at arXiv:1908.03887, or as view-only published version
[27] Shifted cotangent stacks are shifted symplectic,
Annales de la faculté des sciences de Toulouse 28 (2019), no. 1, 67-90.
Freely available at arxiv:1612.08101
[26] A note on the (∞,n)-category of cobordisms (with Claudia Scheimbauer),
Algebraic and Geometric Topology 19 (2019), no. 2, 533-655.
Freely available at arXiv:1509.08906
[25] The Ext algebra of a quantized cycle (with Julien Grivaux),
Journal de l'École polytechnique - Mathématiques 6 (2019), 31-77.
Freely available at arXiv:1711.09402
[24] Shifted Poisson structures and Deformation Quantization (with Tony Pantev, Bertrand Toën, Michel Vaquié and Gabriele Vezzosi),
Journal of Topology 10 (2017), no. 2, 483-584.
Freely available at arXiv:1506.03699
[23] Lagrangian structures on mapping stacks and semi-classical TFTs,
Stacks and Categories in Geometry, Topology, and Algebra, Contemporary Mathematics 643 (2015).
Freely available at arXiv:1306.3235
[22] A trace formula for the quantization of coadjoint orbits (with Florian Naef),
International Mathematical Research Notices 2015 (2015).
Freely available at arXiv:1403.6864
[21] Triviality of the higher formality theorem (with Thomas Willwacher),
Proceedings of the AMS (2015).
Freely available at arXiv:1310.4605
[20] Three lectures on derived symplectic geometry and topological field theories,
Indagationes Mathematicae 25 (2014), no. 5, 926-947, Poisson 2012: Poisson Geometry in Mathematics and Physics.
Freely available on my lecture notes page
[19] On the Lie algebroid of a derived self-intersection (with Andrei Caldararu and Junwu Tu),
Advances in Mathematics 262 (2014), 751-783.
Freely available at arXiv:1306.5260
[18] A PBW theorem for inclusions of (sheaves of) Lie algebroids, 
Rendiconti del Seminario Matematico della Università di Padova 131 (2014), 23-47.
Freely available at arXiv:1205.3214
[17] PBW for an inclusion of Lie algebras (with Andrei Caldararu and Junwu Tu), 
Journal of Algebra 378 (2013), 64-79.
Freely available at arXiv:1010.0985
[16] Caldararu's conjecture and Tsygan's formality (with Carlo A. Rossi and Michel Van den Bergh), 
Annals of Mathematics 176 (2012), no. 2, 865-923.
Freely available at arXiv:0904.4890
[15] Two interacting Hopf algebras of trees (with Kurusch Ebrahimi-Fard and Dominique Manchon),
Advances in Applied Mathematics  47 (2011), no. 2, 282-308.
Freely available at arXiv:0806.2238
[14] Deformation quantization with generators and relations (with Giovanni Felder and Carlo A. Rossi), 
Journal of Algebra 337 (2011), no. 1, 1-12.
Freely available at arXiv:0911.4377
[13] Weak quantization of Poisson structures (with Gilles Halbout), 
Journal of Geometry and Physics 61 (2011), no. 8, 1401-1414.
Freely available at arXiv:0707.1978
[12] Compatibility with cap-products in Tsygan's formality and homological Duflo isomorphism (with Carlo A. Rossi), 
Letters in Mathematical Physics 95 (2011), no. 2, 135-209.
Freely available at arXiv:0805.3444
[11] Bimodules and branes in deformation quantization (with Giovanni Felder, Andrea Ferrario and Carlo A. Rossi), 
Compositio Mathematica 147 (2011), no. 1, 105-160.
Freely available at arXiv:0908.2299
[10] Hochschild (co)homology for Lie algebroids (with Carlo A. Rossi and Michel Van den Bergh), 
International Mathematical Research Notices 2010 (2010), no. 21, 4098-4136.
Freely available at arXiv:0908.2630
[09] Hochschild cohomology and Atiyah classes (with Michel Van den Bergh), 
Advances in Mathematics 224 (2010), no. 5, 1839-1889.
Freely available at arXiv:0708.2725
[08] Global formality at the $G_\infty$-level (with Michel Van den Bergh), 
Moscow Mathematical Journal 10 (2010), no. 1, 31-64.
Freely available at arXiv:0710.4510
[07] Universal KZB equations: the elliptic case (with Benjamin Enriquez and Pavel Etingof), 
Algebra, Arithmetic and Geometry Vol I: in honor of Yu. I. Manin, Progress in Mathematics 269 (2010), 165-266.
Freely available at arXiv:math/0702670
[06] Lectures on tensor categories (with Pavel Etingof); 
IRMA Lectures in Mathematics and Theoretical Physics 12 (2008), 1-38.
Freely available at arXiv:math/0401246
[05] Shoikhet's conjecture and Duflo isomorphism on (co)invariants (with Carlo A. Rossi), 
SIGMA 4 (2008), 060, 17 pages, contribution to the Special Issue on Deformation Quantization.
Freely available at arXiv:0805.2409
[04] Quantization of symplectic dynamical r-matrices and the quantum composition formula (with Anton Alekseev), 
Communications in Mathematical Physics 273 (2007), no. 1, 119-136.
Freely available at arXiv:math/0606498
[03] Formality theorems for Hochschild chains in the Lie algebroid setting (with Vasiliy Dolgushev and Gilles Halbout), 
Journal fur die reine und angewandte Mathematik 612 (2007), 81-127.
Freely available at arXiv:math/0504372
[02] Quantization of formal classical dynamical r-matrices: the reductive case, 
Advances in Mathematics 204 (2006), no. 1, 84-100.
Freely available at arXiv:math/0412042
[01] Formality for Lie algebroids, 
Communications in Mathematical Physics 257 (2005), no. 3, 563-578.
Freely available at arXiv:math/0404265

Minor contributions

[5] Derived symplectic geometry, in Encyclopedia of Mathematical Physics 2nd edition,  
Freely available at arXiv:2308.04210
[4] Hochschild cohomology of smooth algebraic varieties, in Hochschild Cohomology in Algebra, Geometry and Topology,  
Oberwolfach reports 13 (2016), no. 1, 453-455.
Freely available on my lecture notes page
[3] A Derived and Homotopical View on Field Theories, in Mathematical Aspects of Quantum Field Theories (Damien Calaque and Thomas Strobl Eds),  
Mathematical Physics Studies (2015), 1-14.
Available here
[2] Contribution to Formality of cyclic cochains by Thomas Willwacher,  
Advances in Mathematics 231 (2012), no. 2, 624-650.
Freely available at arXiv:0806.4095
[1] From Lie theory to algebraic geometry and back, in Interactions between Algebraic Geometry and Noncommutative Algebra,  
Oberwolfach reports 7 (2010), no. 2.
Freely available on my lecture notes page

Not intended to be published (use with care)

[2] Around Hochschild (co)homology
Habilitation Thesis
[1] Formality theorems for Lie algebroids and quantization of dynamical r-matrices
PhD Thesis
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