Recent publications:

• The weighted projective superspace with weights $+1,−1$ and an analog of the Fubini--Study form. arxiv:2402.11860 (with E. Shemyakova)
• L-infinity bialgebroids and homotopy Poisson structures on supermanifolds. arXiv:1909.04914
• Thick morphisms, higher Koszul brackets, and $L_{\infty}$-algebroids. arXiv:1808.10049 (with H. Khudaverdian)
• Tangent functor on microformal morphisms, and non-linear pullbacks for forms and cohomology.
  J. Geom. Phys. 197, 105105 (2024), https://doi.org/10.1016/j.geomphys.2024.105105, arXiv:1710.04335
• On the Buchstaber--Rees theory of "Frobenius n-homomorphisms'' and its generalization.
  Contemporary Mathematics 789 (2023), https://doi.org/10.1090/conm/789/15843, arXiv:2002.02395 [math.RA] (with H. Khudaverdian)
• On super Plücker embedding and cluster algebras.
  Selecta Math. N.S. 28, 39 (2022), https://doi.org/10.1007/s00029-021-00756-w, (with E. Shemyakova)
• On differential operators over a map, thick morphisms of supermanifolds, and symplectic micromorphisms.
  Differential Geom. Appl. 74 (2021), 101704, DOI: 10.1016/j.difgeo.2020.101704, arXiv:2009.12458 [math.DG] (with E. Shemyakova)
• Thick morphisms of supermanifolds, quantum mechanics, and spinor representation.
  J. Geom. Phys. 148 (February 2020), 103540, DOI: 10.1016/j.geomphys.2019.103540, arXiv:1909.00290 (with H. Khudaverdian)
• Graded geometry, $Q$-manifolds, and microformal geometry.
  Fortschr. Phys. 67 (2019), 1910023 DOI: 10.1002/prop.201910023. arXiv:1903.02884
• Differential operators on the algebra of densities and factorization of the generalized Sturm-Liouville operator.
  Lett. Math. Phys. 109, Issue 2 (2019), 403-421. DOI: 10.1007/s11005-018-1113-9. arXiv:1710.09542 (with E. Shemyakova.)
• Microformal geometry and homotopy algebras.
  Proc. Steklov Inst. Math. 302 (2018), 88-129. SharedIt link: https://rdcu.be/bflnC arXiv:1411.6720
• Differential operators on the superline, Berezinians, and Darboux transformations.
  Lett. Math. Phys. 107, Issue 9 (2017), 1689-1714. arXiv:1605.07286 (with S. Li and E. Shemyakova)
• "Nonlinear pullbacks" of functions and L_∞-morphisms for homotopy Poisson structures.
  J. Geom. Phys. 111 (2017), 94-110. arXiv:1409.6475
• Quantum microformal morphisms of supermanifolds: an explicit formula and further properties. arXiv:1512.04163
• On volumes of classical supermanifolds.
  Sbornik: Mathematics 207 (11) (2016), 1512-1536. (Short version: arXiv:1503.06542).
• Thick morphisms of supermanifolds and oscillatory integral operators.
  Russian Math. Surveys 71 (4) (2016), 784-786. arXiv:1506.02417
• Darboux transformations for differential operators on the superline.
  Russian Math. Surveys 70 (6) (2015), 207-208. arXiv:1505.05194 (with S. Hill and E. Shemyakova)
• Geometric constructions on the algebra of densities.
  In: Topology, Geometry, Integrable Systems, and Mathematical Physics: Novikov's Seminar 2012--2014, V. M. Buchstaber, B. A. Dubrovin, and I. M. Krichever, eds., AMS Translations, Ser. 2, vol. 234, Amer. Math. Soc., Providence, RI, 2014, p. 221-243. arXiv:1310.0784 (With H. Khudaverdian.)
• Vector fields on mapping spaces and a converse to the AKSZ construction. arXiv:1211.6319
• Book: Geometric Integration Theory on Supermanifolds. 2nd expanded edition. Cambridge Scientific Publ., 2014. (Vol. 3 in the series: Classic Reviews in Mathematics and Mathematical Physics.)
• Geometry of differential operators of second order, the algebra of densities, and groupoids.
  J. Geom. Phys. 64 (2013), 31--53. (With H. Khudaverdian.) arXiv:1112.5379
• $Q$-manifolds and Mackenzie theory,
  Comm. Math. Phys. 315 (2) (2012), 279--310. arXiv:1206.3622
• Felix Alexandrovich Berezin and his work.
  In: Geometric Methods in Physics, P. Kielanowski, S. Twareque Ali, A. Odzijewicz, M. Schlichenmaier, Th. Voronov, eds. Trends in Mathematics. Springer Basel 2013, pp. 3-33. arXiv:1202.3930. (With A. Karabegov and Yu. Neretin.)
• $Q$-manifolds and higher analogs of Lie algebroids.
  In: XXIX Workshop on Geometric Methods in Physics. AIP CP 1307, pp. 191--202, Amer. Inst. Phys., Melville, NY, 2010, arXiv:1010.2503.
• A short proof of the Buchstaber-Rees theorem.
  Phil. Trans. R. Soc. A. 369 (1939) (2011), 1334-1345. arXiv:1010.2488. (With H. Khudaverdian.).
• On a non-Abelian Poincaré lemma.
  Proc. Amer. Math. Soc. 140 (2012), 2855-2872. arXiv:0905.0287.
• Higher Poisson brackets and differential forms.
  In: Geometric Methods in Physics. AIP Conference Proceedings 1079, American Institute of Physics, Melville, New York, 2008, 203-215. arXiv:0808.3406. (With H. Khudaverdian.)
• Differential forms and odd symplectic geometry.,
  In: Geometry, Topology and Mathematical Physics. S. P. Novikov seminar: 2006-2007, V. M. Buchstaber and I. M. Krichever, eds. AMS Translations, Ser. 2, Vol. 224, Amer. Math. Soc., Providence, RI, 2008, 159-171, arXiv:math.DG/0606560. (With H. Khudaverdian.)
• Operators on superspaces and generalizations of the Gelfand-Kolmogorov theorem.
  In: XXVI Workshop on Geometric Methods in Physics. AIP Conference Proceedings 956, American Institute of Physics, Melville, New York, 2007, 149-155. arXiv:0709.4402. (With H. Khudaverdian.)
• $Q$-manifolds and Mackenzie theory: an overview.
  ESI preprint 1952, arXiv:0709.4232
• On generalized symmetric powers and a generalization of Kolmogorov-Gelfand-Buchstaber-Rees theory.
  Russian Math. Surveys 62 (3) (2007), 209-210, arXiv:math.RA/0612072. (With H. Khudaverdian.)
• Mackenzie theory and $Q$-manifolds. arXiv:math.DG/0608111.
• New facts about Berezinians.
  In: Supersymmetries and Quantum Symmetries 2005. Proceedings of International Workshop, Joint Institute of Nuclear Research, Dubna, 27-31 July 2005, E. Ivanov and B. Zupnik, eds., Dubna, 2006, 393-398, arXiv:math-ph/0512031. (With H. Khudaverdian.)
• Higher derived brackets for arbitrary derivations.
  Travaux Mathématiques XVI (2005), 163-186, arXiv:math.QA/0412202
• Berezinians, exterior powers and recurrent sequences.
  Lett. Math. Phys. 74 (2005), Number 2, November 2005 [Berezin Memorial Volume], 201-228, arXiv:math.DG/0309188. (With H. Khudaverdian.)
• Higher derived brackets and homotopy algebras.
  J. Pure and Appl. Algebra. 202 (2005), Issues 1-3, 1 November 2005, 133-153, arXiv:math.QA/0304038
• Geometry of differential operators, odd Laplacians, and homotopy algebras,
  J. Nonlinear Math. Phys. 11 (2004), Supplement, 217-227, arXiv:math.DG/0402292. (With H. Khudaverdian.)
• An alternative form of the Helmholtz criterion in the inverse problem of calculus of variations,
  Lett. Math. Phys. 67 (2) (2004), 103-110, arXiv:math.DG/0308179
• Geometry of differential operators, and odd Laplace operators.
  Russian Math. Surveys 58(1) (2003), 197-198, arXiv:math.DG/0301236. (With H. Khudaverdian.)
• On odd Laplace operators. II,
  In: Geometry, Topology and Mathematical Physics. S. P. Novikov's seminar: 2002 - 2003, V. M. Buchstaber and I. M. Krichever, eds. AMS Translations, Ser. 2, Vol. 212, Amer. Math. Soc., Providence, RI, 2004, 179-205, arXiv:math.DG/0212311. (With H. Khudaverdian.)
• On odd Laplace operators.
  Lett. Math. Phys. 62 (2002), 127-142, arXiv:math.DG/0205202. (With H. Khudaverdian.)
• Graded manifolds and Drinfeld doubles for Lie bialgebroids.
  In: Quantization, Poisson Brackets and Beyond, Theodore Voronov, ed., Contemp. Math., Vol. 315, Amer. Math. Soc., Providence, RI, 2002, 131-168, arXiv:math.DG/0105237.
• On complexes related with calculus of variations.
  J. Geom. Phys. 44 (2-3) (2002), 221-250, arXiv:math.DG/0105223. (With H. Khudaverdian.)
• Dual forms on supermanifolds and Cartan calculus.
  Comm. Math. Phys. 228 (1) (2002), 1-16, arXiv:math.DG/9912192.
• Cartan calculus for dual forms.
  Russian Math. Surveys 56(2) (2001), 421-422.
• Quantization of forms on the cotangent bundle.
  Comm. Math. Phys. 205 (2) (1999), 315-336, arXiv:math.DG/9809130.

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Last modified: 14 (27) February 2024 Ted Voronov