Alexander A. Voronov

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Books and Collections:

  1. Higher Structures in Topology, Geometry and Physics (coedited with R. M. Kaufmann and M. Markl), Contemp. Math. AMS, Providence, RI, 2023, to appear.
  2. String topology and cyclic homology (with R. L. Cohen and K. Hess), Adv. Courses in Math. CRM Barcelona. Birkhäuser, Basel, 2006.
  3. Operads: Proceedings of Renaissance Conferences (coedited with J.-L. Loday and J. Stasheff), Contemp. Math., vol. 202. AMS, Providence, RI, 1997.

Popular Science Notes:

  1. What IPMU stands for. Kavli IPMU News. 45 (2019), 9.
  2. λ-Adic topology. Kavli IPMU News. 42 (2018), 22. Version in Japanese.
  3. What is a WDVV-algebra? Kavli IPMU News. 42 (2018), 16. Version in Japanese.
  4. Hey, tell me what you do in research! Kavli IPMU News. 37 (2017), 14. Version in Japanese.
  5. In search of solitons in Amsterdam. Kavli IPMU News. 34 (2016), 13. Version in Japanese.
  6. Urashima effect: a version. Kavli IPMU News. 31 (2015), 22-23. Version in Japanese.


  1. Mysterious Triality and M-Theory (with H. Sati), Preprint IPMU23-0001, 69 pages, arXiv:2212.13968 [hep-th], submitted.
  2. Mysterious Triality and Rational Homotopy Theory (with H. Sati), Commun. Math. Phys. 400 (2023), no. 3, 1915-1960, arXiv:2111.14810 [hep-th].
  3. The supermoduli space of genus zero super Riemann surfaces with Ramond punctures (with N. Ott), 45 pp., Journal of Geometry and Physics, 185, (2023), 104726, arXiv:1910.05655 [math.AG].
  4. On the BV structure on the cohomology of moduli space (with S. Sakalli), Pure and Applied Mathematics Quarterly 16 (2020), no. 3, 755-773, Journal Online, arXiv:1912.13045 [math.AG].
  5. Quantizing deformation theory II, Pure and Applied Mathematics Quarterly 16 (2020), no. 1, 125-152, Journal Online, arXiv:1806.11197 [math.QA].
  6. On homotopy Lie bialgebroids (with D. Bashkirov), Preprint IPMU16-0198, 21 pp., arXiv:1612.02026 [math.QA].
  7. The MV formalism for IBL- and BV-algebras (with M. Markl), Lett. Math. Phys. 107 (2017), no. 8, 1515-1543, Springer Online First, arXiv:1511.01591 [math.QA].
  8. Categorification of Dijkgraaf-Witten Theory (with A. Sharma), Adv. Theor. Math. Phys. 21 (2017), no. 4, 1023-1061, arXiv:1511.00295 [math.AT].
  9. The BV formalism for L-algebras (with D. Bashkirov), J. Homotopy Relat. Struct. 12 (2017), no. 2, 305-327, arXiv:1410.6432 [math.QA].
  10. r-Matrices, triangular L-bialgebras, and quantum groups (with D. Bashkirov). Geometric Methods in Physics. XXXIII Workshop 2014, 39-47, Trends in Mathematics, Birkhäuser Boston, Inc., Boston, MA, 2015, arXiv:1412.2413 [math.QA].
  11. A higher category of cobordisms and topological quantum field theory (with M. Feshbach), Preprint IPMU11-0143, 37 pp., arXiv:1108.3349 [math.QA].
  12. Open-closed moduli spaces and related algebraic structures (with E. Harrelson and J. J. Zuniga). Lett. Math. Phys. 94 (2010), no. 1, 1-26, arXiv:0709.3874[math.QA].
  13. Graph homology: Koszul and Verdier duality (with A. Lazarev), Adv. Math. 218 (2008), no. 6, 1878-1894, arXiv:math/0702313 [math.QA].
  14. Notes on string topology (with R. L. Cohen), String topology and cyclic homology, 1-95, Adv. Courses Math. CRM Barcelona, Birkhäuser, Basel, 2006, arXiv:math/0503625 [math.GT].
  15. The canonical delooping machine (with B. Badzioch and K. Chung), J. of Pure and Applied Algebra 208 (2007), no. 2, 531-540, arXiv:math/0403098 [ math.AT].
  16. On Kontsevich's Hochschild cohomology conjecture (with P. Hu and I. Kriz), Compos. Math. 142 (2006), no. 1, 143-168, arXiv:math/0309369 [math.AT].
  17. PROPped-up graph cohomology (with M. Markl). Algebra, arithmetic, and geometry: in honor of Yu. I. Manin. Vol. II, 249-281, Progr. Math., 270, Birkhäuser Boston, Inc., Boston, MA, 2009, arXiv:math/0307081 [math.QA].
  18. Notes on universal algebra. Graphs and Patterns in Mathematics and Theoretical Physics (M. Lyubich and L. Takhtajan, eds.), Proc. Sympos. Pure Math., vol. 73. AMS, Providence, RI, 2005, pp. 81-103, arXiv:math/0111009 [math.QA].
  19. Homotopy Gerstenhaber algebras. Conference Moshé Flato 1999 (G. Dito and D. Sternheimer, eds.), vol. 2. Kluwer Academic Publishers, the Netherlands, 2000, pp. 307-331, arXiv:math/9908040 [math.QA].
  20. The Swiss-cheese operad, Homotopy invariant algebraic structures (Baltimore, MD, 1998), Contemp. Math., vol. 239. AMS, Providence, RI, 1999, pp. 365-373, arXiv:math/9807037 [math.QA].
  21. Cohomology of conformal algebras (with B. Bakalov and V. G. Kac), Comm. Math. Phys. 200 (1999), 561-598, arXiv:math/9803022 [math.QA].
  22. Stability of the rational homotopy type of moduli spaces, Higher homotopy structures in topology and mathematical physics (Poughkeepsie, NY, 1996), Contemp. Math., vol. 227. AMS, Providence, RI, 1999, pp. 315-321, alg-geom/9708019.
  23. Semi-infinite induction and Wakimoto modules, Amer. J. Math. 121 (1999), no. 5, 1079-1094, q-alg/9704020.
  24. Quantizing Poisson manifolds. Perspectives on Quantization (L. A. Coburn and M. A. Rieffel, eds.), Contemp. Math., vol. 214. AMS, Providence, RI, 1998, pp. 189-195, q-alg/9701017.
  25. Semiquantum geometry (with N. Reshetikhin and A. Weinstein). Algebraic geometry, 5. J. Math. Sci. 82 (1996), no. 1, 3255-3267. q-alg/9606007.
  26. Homotopy Gerstenhaber algebras and topological field theory (with T. Kimura and G. Zuckerman). Operads: Proceedings of Renaissance Conferences (J.-L. Loday, J. Stasheff, and A. A. Voronov, eds.), Contemp. Math., vol. 202. AMS, Providence, RI, 1997, pp. 305-334, q-alg/9602009.
  27. Homology of moduli spaces of curves and commutative homotopy algebras (with T. Kimura and J. Stasheff). The Gelfand Mathematical Seminars, 1993-1995. Edited by I. Gelfand, J. Lepowsky, and M. M. Smirnov. Birkhäuser, Boston, Inc., Boston, MA, 1996, pp. 151-170, alg-geom/9502006.
  28. Cohomology and deformation of Leibniz pairs (with M. Flato and M. Gerstenhaber). Letters in Mathematical Physics 34(1), 77-90 (1995), q-alg/9502006.
  29. The cohomology of algebras over moduli spaces (with T. Kimura). In: The Moduli Space of Curves (R. Dijkgraaf, C. Faber, and G. van der Geer, eds.) Progress in Mathematics, vol. 129. Birkhäuser, Boston, MA, 1995, pp. 305-334, hep-th/9410108.
  30. Homotopy G-algebras and moduli space operad (with M. Gerstenhaber). Internat. Math. Research Notices 141-153 (1995), hep-th/9409063.
  31. Higher-order operations on the Hochschild complex (with M. Gerstenhaber). Functional Anal. Appl. 29(1), 1-6 (1995) [Russian version]  [English version].
  32. Topological field theories, string backgrounds and homotopy algebras. In: Proceedings of the XXIInd International Conference on Differential Geometric Methods in Theoretical Physics, Ixtapa-Zihuatanejo, Mexico (J. Keller and Z. Oziewicz, eds.) Advances in Applied Clifford Algebras (Proc. Suppl.) 4(S1) 167-178 (1994), hep-th/9401023.
  33. On operad structures of moduli spaces and string theory (with T. Kimura and J. Stasheff). Comm. Math. Phys. 171, 1-25 (1995), hep-th/9307114.
  34. Semi-infinite cohomology of Lie algebras. Proc. Sympos. Pure Math. 56, part 2, 401-415 (1994)
  35. Semi-infinite homological algebra. Invent. Math. 113, 103-146 (1993)
  36. BRST cohomology: a new derived functor. In: XXth International Conference on Differential Geometric Methods in Theoretical Physics, vol. 2. World Scientific, Singapore, 1992, pp. 905-912.
  37. Complex divisors on algebraic curves and some applications to string theory. Contemp. Math. 131, part 3, 515-522 (1992), alg-geom/9202028.
  38. A unified approach to string scattering amplitudes. Comm. Math. Phys. 131, 179-218 (1990). Correction: 140, 415-416 (1991).
  39. Superconformal geometry and string theory (with A. A. Rosly and A. S. Schwarz). Comm. Math. Phys. 120(3), 437-450 (1989).
  40. Geometry of superconformal manifolds (with A. A. Rosly and A. S. Schwarz). Comm. Math. Phys. 119, 129-152 (1988).
  41. Supercellular partitions of flag superspaces (with Yu. I. Manin). Current problems in mathematics. Newest results, USSR Acad. Sci., Moscow. 32, 27-70 (1988). (in Russian). English translation: J. Soviet Math. 51(1), 2083-2108 (1990).
  42. Elements of supergeometry (with Yu. I. Manin and I. B. Penkov). Current problems in mathematics. Newest results, USSR Acad. Sci., Moscow. 32, 3-26 (1988) (in Russian). English translation: J. Soviet Math. 51(1), 2069-2082 (1990).
  43. A formula for Mumford measure in superstring theory. Functional Anal. Appl. 22(2), 139-140 (1988) [Russian version]  [English version].
  44. Relative disposition of the Schubert supervarieties and resolution of their singularities. Functional Anal. Appl. 21, 62-64 (1987).
  45. Schubert supercells (with Yu. I. Manin). Functional Anal. Appl. 18, 329-330 (1985).
  46. Mappings of supermanifolds. Theoret. and Math. Phys. 60, 660-664 (1985).

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Alexander A. Voronov
Last modified: (2023-09-18 04:47:01 CDT)