Publications
Work in progress
- Factorization homology as a fully extended TFT (with Claudia Scheimbauer)
- Ellipsitomic associators (with Martin Gonzalez)
- Factorization algebras arising from lattice models (with Giovanni Felder)
- E_n-algebras and vertex models (with Damien Lejay)
- Shifted symplectic groupoids (with Pavel Safronov)
- AKSZ construction as a fully extended TFT (with Claudia Scheimbauer and Rune Haugseng)
- Shifted symplectic reduction and the BV formalism (with Mathieu Anel)
Preprints
- [3] On the universal ellipsitomic KZB connection (with Martin Gonzalez),
- Freely available at arXiv:1908.03887
- [2] Derived stacks in symplectic geometry,
- Freely available at arXiv:1802.09643
- [1] Formal moduli problems and formal derived stacks (with Julien Grivaux),
- Freely available at arXiv:1802.09556
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
- [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 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).
[2] Formality theorems for Lie algebroids and quantization of dynamical r-matrices (PhD Thesis).