Publications

Work in progress

• From Lie theory to algebraic geometry and back (with Andrei Caldararu and Junwu Tu)
  
• Factorization algebras arising from lattice models
• A note on generalized swiss-cheese operads
  
• Shifted cotangent bundle valued Chern-Simons theories and
  formality theorems (with Gregory Ginot)
  

Preprints

[3] A PBW theorem for inclusions of (sheaves of) Lie algebroids, 

 Freely available Here

[2] PBW for an inclusion of Lie algebras (with Andrei Caldararu and Junwu Tu), 

 Freely available at arXiv:1010.0985

[1] Contribution to Formality of cyclic cochains by Thomas Willwacher, 

Freely available at arXiv:0806.4095

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

[16] Caldararu's conjecture and Tsygan's formality (with Carlo A. Rossi and Michel Van den Bergh), 

To appear in Annals of Mathematics
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