Papers and preprints:
(Most of the links below are to the Front for the Mathematics ArXiv; click here for MathSci reviews.)

• A geometric characterization of N-manifolds and the Frobenius theorem (with M. Cueca and R. Mehta). Preprint.

• Lie groupoids (with M. del Hoyo). Contribution for the Encyclopedia of Mathematical Physics, 2023.

• Graded geometry and generalized reduction (with A. Cattaneo, R. Mehta and M. Zambon). Preprint .

• Courant-Nijenhuis algebroids (with T. Drummond and C. Netto). J. Geom. Physics 192 (2023).

• Dirac structures and Nijenhuis operators (with T. Drummond and C. Netto). Math. Z. 302 (2022), 875–915.

• Poisson double structures (with A. Cabrera and M. del Hoyo). J. Geom. Mech. 14 (2022), 151–178.

• Morita equivalence of formal Poisson structures (with I. Ortiz and S. Waldmann). Int. Math. Res. Not. IMRN 2022, no. 18, 13703–13752.

• Dirac geometry and integration of Poisson homogeneous spaces (with D. Iglesias-Ponte and J.-H. Lu). To appear in J. Differential Geom.

• Deformation spaces and normal forms around transversals (with F. Bischoff, H. Lima, E. Meinrenken). Compos. Math. 156 (2020), 697-–732.

• Principal actions of stacky Lie groupoids (with F. Noseda and C. Zhu). Intern. Math. Res. Notices , IMRN 2020, no. 16, 5055--5125.

• Lie theory of multiplicative tensors (with T. Drummond). Math. Annalen 375 (2019), 1489-–1554..

• Splitting theorems for Poisson and related structures (with H. Lima and E. Meinrenken). J. Reine Angew. Math. (Crelle's Journal) , 754 (2019), 281–-312.

• On higher Dirac structures (with N. Martinez and R. Rubio). Intern. Math. Res. Notices , IMRN 2019, no. 5, 1503-–1542.

• Picard groups of Poisson manifolds (with R. L. Fernandes). J. Differential Geom. , 109 (2018), 1--38.

• Lie theory of vector bundles, Poisson geometry and double structures (with A. Cabrera and M. del Hoyo). Proceedings of the International Congress of Mathematical Physics, Santiago, 2015.

• Vector bundles over Lie groupoids and algeboids (with A. Cabrera and M. del Hoyo). Advances in Math. , 290 (2016), 163--207.

• Generalized Kaehler geometry of instanton moduli spaces (with G. Cavalcanti and M. Gualtieri). Comm. Math. Physics , 333 (2015), 831--860.

• Multisymplectic geometry and Lie groupoids (with A. Cabrera and D. Iglesias), in Geometric Mechanics: the Legacy of Jerry Marsden, Fields Institute Communications vol. 73, 2015.

• Lie groupoids and the Froelicher-Nijenhuis bracket (with T. Drummond). Bull. of Brazilian Math. Soc. , 44 (2013), 709--730.

• A brief introduction to Dirac manifolds , In: Geometric and topological methods for quantum field theory , Cambridge University Press, 2013. Printed version .

• Multiplicative forms at the infinitesimal level (with A. Cabrera). Math. Annalen 353 (2012), 663--705. Online version.

• Symmetries and reduction of multiplicative 2-forms (with A. Cabrera). J. Geom. Mech., 4 (2012), 111--127.
• Morita equivalence and characteristic classes of star products (with V. Dolgushev and S. Waldmann). J. Reine Angew. Math. (Crelle's Journal) 662 (2012), 95--163.

• Strong and covariant Morita equivalences in deformation quantization (with S. Waldmann), Travaux Mathematiques, Fasc. XX (2012), 121--143. Special issue based on the Commemorative Colloquium dedicated to Nikolai Neumaier, Mulhouse, France, 2011.

• Classifying Morita equivalent star products (with S. Waldmann), In: Topics in noncommutative geometry , Clay Mathematics Proceedings, vol. 16, Amer. Math. Soc., Providence, RI, 2012, pp. 1-17.

• Pure spinors on Lie groups (with A. Alekseev and E. Meinrenken). Asterisque. No. 327, p. 129-197, 2010.

• Linear and multiplicative 2-forms (with A. Cabrera and C. Ortiz). Lett. in Math. Phys. 90 (2009), 59--83.

• Dirac geometry, quasi-Poisson actions and D/G-valued moment maps (with M. Crainic). J. Differential Geometry 82 (2009), 501--566.

• Courant morphisms and moment maps (with D. Iglesias Ponte and P. Severa). Math. Research Letters. 16 (2009), 215--232.

• Generalized Kahler and hyper-Kahler quotients (with G. Cavalcanti and M. Gualtieri). Contemporary Mathematics, 450, American Mathematical Society, 2008, 61--77.

• Reduction of Courant algebroids and generalized complex structures (with G. Cavalcanti and M. Gualtieri ). Advances in Math. 211 (2007), 726--765.
• Quasi-Poisson structures as Dirac structures (with M. Crainic and P. Severa). Travaux Mathematiques , Fasc. XVI (2005), 41--52.
• Induction of representations in deformation quantization (with S. Waldmann). Noncommutative geometry and physics, 65--76, World Sci. Publ., Hackensack, NJ, 2005.
• Hermitian star products are completely positive deformations (with S. Waldmann). Lett. Math. Phys., 72 (2005), 143-152.
• Completely positive inner products and strong Morita equivalence (with S. Waldmann), Pacific J. Math., 222 (2005), 201-236.
• Generalizing symmetries in symplectic geometry , Mat. Contemp. 28 (2005), 111--132.
• Poisson geometry and Morita equivalence (with A. Weinstein), in Poisson geometry, deformation quantisation and group representations, London Mathematical Society Lecture Notes series, 323, Cambridge Univ. Press (2005).
• Dirac structures, moment maps and quasi-Poisson manifolds (with M. Crainic), in The breadth of symplectic and Poisson geometry , Progr. Math 232, Birkhauser, 2005, 1-40. (Festschrift in honor of Alan Weinstein).
• On gauge transformations of Poisson structures , in Quantum Field Theory and Noncommutative Geometry, Lect. Notes Phys., 662 Springer-Verlag (2005), 89-112.
• Picard groups in Poisson geometry (with A. Weinstein), Moscow Math. J. 4 (2004), 39-66. Dedicated to Pierre Cartier.
• Integration of twisted Dirac brackets (with M. Crainic, A. Weinstein and C. Zhu), Duke Math. J., 123 (2004), 549--607. MSRI Preprint 2003-01
• Bimodule deformations, Picard groups and contravariant connections (with S.Waldmann), K-Theory 31 (2004), 1-37. MSRI Preprint 2002-26.
• Gauge equivalence of Dirac structures and symplectic groupoids (with O. Radko), Ann. Inst. Fourier (Grenoble), 53 (2003), 309-337. (MSRI Preprint 2002-10)
• The characteristic classes of Morita equivalent star products on symplectic manifolds (with S. Waldmann), Comm. Math. Phys. 228.1 (2002), 103-121.
• Semiclassical geometry of quantum line bundles and Morita equivalence of star products , Intern. Math. Res. Notices , 16 (2002) 82 1--846.
• Poisson vector bundles, contravariant connections and deformations, (pdf file), In Y. Maeda (ed.) et al.: Noncommutative geometry and string theory. Prog. Theo. Phys. Suppl. 144 (2001), 26-37.
• *- Ideals and formal Morita equivalence of *-algebras (with S. Waldmann), Internat. J. Math. 12.5 (2001), 555-577.
• Algebraic Rieffel induction, formal Morita equivalence, and applications to deformation quantization (with S. Waldmann), J. Geom. Phys. 37.4 (2001), 307--364.

• Deformation quantization of Hermitian vector bundles (with S. Waldmann), Lett. Math. Phys. 53.4 (2000), 349--365.
• On positive deformations of *-algebras (with S. Waldmann), In G. Dito and D. Sternheimer (Eds.): Conference Moshe Flato 1999. Quantization, Deformations and Symmetries. Mathematical Physics Studies 22, 69-80. Kluwer, 2000.

Other publications...

• Bursztyn, Henrique; Fernandes, Rui L.: A conversation with Alan Weinstein. Notices Amer. Math. Soc. 70 (2023), no. 1, 125–133.

• Androulidakis, Iakovos; Bursztyn, Henrique; Marrero, Juan-Carlos; Weinstein, Alan.: Preface to special issue in honor of Kirill C. H. Mackenzie. J. Geom. Mech. 13 (2021), no. 3, i–ix.

• Bursztyn, H.; Futorny, V.; Hernandez Rizzo, P.; Iusenko, K.; Ortiz, C.: Workshop on geometry in algebra and algebra in geometry: opening note. Held at the Universidad de Antioquia, Medellin, 2019. São Paulo J. Math. Sci. 15 (2021), no. 2, 615–616.

• Mathai, Varghese; Thiang, Guo Chuan; Hekmati, Pedram; Bursztyn, Henrique; Bouwknegt, Peter; Baraglia, David [editors]. Foreword: String geometries, dualities and topological matter. J. Geom. Phys. 138 (2019), 331–332.

• H Bursztyn and R. I. Oliveira: IMPA, European Math. Society Newsletter, June 2017.

• H. Bursztyn, R. Fernandes, J.-H. Lu and A. Weinstein: Poisson 2010: Poisson geometry in mathematics and physics, special issue of the Bulletin of the Brazilian Mathematical Society, volume 42, 2011.

• Introdução a Geometria Simplética (with L. Macarini), minicourse at the XIV Brazilian School of Differential Geometry, Salvador, July 2006.

PhD Thesis:

• Morita equivalence in deformation quantization. pdf file . U.C. Berkeley, May 2001.

Online Lecture videos

• Minicourse on Poisson geometry, Poisson 2022 advanced school, CRM, Barcelona, 2022.
• Revisiting and extending Poisson-Nijenhuis structures, Geometria em Lisboa, 2021.
• Poisson geometry and double Lie theory, VII School and Workshop on Lie theory, 2021.
• Relating Morita equivalence in algebra and geometry via deformation quantization. Global noncommutative geometry seminar, 2021.
• Morita equivalence of formal Poisson structures and links with deformation quantization. Global Poisson Webinar, 2020.
• A matemática da quantização, Palestra de divulgação, Colóquio Brasileiro de Matemática, 2015.
• A matemática dos nós, Palestra de divulgação, IMPA, 2014.
• Symplectic geometry in degree 2, Conferencia IMPA 60 anos, 2012.
• Minicourse on multiplicative structures on Lie groupoids, Poisson 2012, U. Utrecht.
• B-fields, quantization and Morita equivalence, talk at the workshop on Symplectic and Poisson Geometry in interaction with Algebra, Analysis and Topology (in honor of Alan Weinstein), MSRI, Berkeley, May 2010.
• Reduction of Courant algebroids, talk at Poisson geometry in mathematics and physics, Tokyo, June 2006.
• Semiclassical geometry of quantum line bundles and Morita equivalence of star products, talk at the workshop on Quantization and Noncommutative Geometry at MSRI, April 2001.