## Damien Calaque

Professeur à l'Université de Montpellier - Membre de l'Institut Universitaire de France

IMAG - Case courrier 051 - 34095 Montpellier cedex 5 - France

Mel : damien.calaque[at]umontpellier.fr
Tel : +33 4 67 14 38 41

## Publications

### Work in progress

• Factorization homology as a fully extended TFT (with Claudia Scheimbauer)
• Twisted elliptic KZB equations and elliptic MZVs at torsion points (with Martin Gonzales)
• Factorization algebras arising from lattice models (with Giovanni Felder)
• Asymptotically locally constant factorization algebras (with Damien Lejay)
• Shifted symplectic groupoids

### Preprints

[2] The Ext algebra of a quantized cycle (with Julien Grivaux),
Freely available at arXiv:1711.09402
[1] A note on the $(\infty,n)$-category of cobordisms (with Claudia Scheimbauer),
Freely available at arXiv:1509.08906

### Books

[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

### Articles

[25] Shifted cotangent stacks are shifted symplectic,
to appear in Annales de la Faculté des Sciences de Toulouse (2017).
Freely available at arxiv:1612.08101
[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 Näf),
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

[2] 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
[1] Contribution to Formality of cyclic cochains by Thomas Willwacher,
Advances in Mathematics 231 (2012), no. 2, 624-650.
Freely available at arXiv:0806.4095

#### Not intended to be published

[1] Around Hochschild (co)homology (Habilitation Thesis).

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