Research

My main mathematical interests are in the fields of operads, as well as in their applications to algebraic topology and homological algebra. I am especially interested in the study of configuration spaces of manifolds, their links to graph complexes, and the invariants they define. These days, I am also interested in the representation stability phenomenon.

See also: arXiv, HAL, MathSciNet, zbMATH, ORCID.

Preprints

  1. Plethysm for characters of relative operads and PROPs

    Authors
    N. I., Erik Lindell.
    Publication
    Preprint v1, 32 p.
    Online on
    Online on .
    Full text
    Full text.
    arXiv:2505.05910
    arXiv:2505.05910.
    hal-05061606
    hal-05061606.
    Source
    Source.

  2. Configuration Spaces of Surfaces

    Authors
    Ricardo Campos, N. I., Thomas Willwacher.
    Publication
    Preprint v2, 50 p.
    Online on
    Online on .
    Updated on
    Updated on .
    Full text
    Full text.
    arXiv:1911.12281
    arXiv:1911.12281.
    hal-02423726
    hal-02423726.

  3. A model for framed configuration spaces of points

    Authors
    Ricardo Campos, Julien Ducoulombier, N. I., Thomas Willwacher.
    Publication
    Preprint v2, 47 p.
    Online on
    Online on .
    Updated on
    Updated on .
    Full text
    Full text.
    arXiv:1807.08319
    arXiv:1807.08319.
    hal-03835341
    hal-03835341.

Publications

  1. Homotopy Prefactorization Algebras

    Authors
    N. I., Eugene Rabinovich.
    Publication
    In: Res. Math. Sci. 11.45 (2024).
    Online on
    Online on .
    Accepted on
    Accepted on .
    Updated on
    Updated on .
    Full text
    Full text.
    10.1007/s40687-024-00456-9
    10.1007/s40687-024-00456-9.
    arXiv:2304.13011
    arXiv:2304.13011.
    hal-04082483
    hal-04082483.
    MR4763063
    MR4763063.
    Zbl07875603
    Zbl07875603.

  2. Non-formality of Voronov's Swiss-Cheese operads

    Authors
    N. I., Renato Vasconcellos Vieira.
    Publication
    In: Q. J. Math. 75.1 (2024), pp. 63-95.
    Online on
    Online on .
    Accepted on
    Accepted on .
    Updated on
    Updated on .
    Full text
    Full text.
    10.1093/qmath/haad041
    10.1093/qmath/haad041.
    arXiv:2303.16979
    arXiv:2303.16979.
    hal-04053257
    hal-04053257.
    MR4732946
    MR4732946.
    Zbl07936839
    Zbl07936839.
    Source
    Source.

  3. Real Homotopy of Configuration Spaces: Peccot Lecture, Collège de France, March & May 2020

    Author
    N. I.
    Publication
    Lecture Notes in Mathematics 2303. Cham: Springer, 2022. 210 pp. ISBN: 978-3-031-04427-4.
    Online on
    Online on .
    Accepted on
    Accepted on .
    Updated on
    Updated on .
    10.1007/978-3-031-04428-1
    10.1007/978-3-031-04428-1.
    hal-03821309
    hal-03821309.
    MR4461096
    MR4461096.
    Zbl07529469
    Zbl07529469.

  4. Boardman–Vogt resolutions and bar/cobar constructions of (co)operadic (co)bimodules

    Authors
    Ricardo Campos, Julien Ducoulombier, N. I.
    Publication
    In: High. Struct. 5.1, pp. 293–366 (2021), 74 pages.
    Online on
    Online on .
    Accepted on
    Accepted on .
    Updated on
    Updated on .
    Full text
    Full text.
    10.21136/HS.2021.09
    10.21136/HS.2021.09.
    arXiv:1911.09474
    arXiv:1911.09474.
    hal-01786218
    hal-01786218.
    MR4367224
    MR4367224.
    Zbl7482172
    Zbl7482172.

  5. Formality of a higher-codimensional Swiss-Cheese operad

    Author
    N. I.
    Publication
    In: Algebr. Geom. Topol. 22.1 (2022), pp. 55–111.
    Online on
    Online on .
    Accepted on
    Accepted on .
    Updated on
    Updated on .
    Full text
    Full text.
    10.2140/agt.2022.22.55
    10.2140/agt.2022.22.55.
    arXiv:1809.07667
    arXiv:1809.07667.
    hal-01878406
    hal-01878406.
    MR4413816
    MR4413816.
    Zbl07518301
    Zbl07518301.

  6. Curved Koszul duality of algebras over unital versions of binary operads

    Author
    N. I.
    Publication
    J. Pure Appl. Algebra 227.3 (2023).
    Online on
    Online on .
    Accepted on
    Accepted on .
    Updated on
    Updated on .
    Full text
    Full text.
    10.1016/j.jpaa.2022.107208
    10.1016/j.jpaa.2022.107208.
    arXiv:1805.01853
    arXiv:1805.01853.
    hal-01786218
    hal-01786218.
    MR4477956
    MR4477956.
    Zbl07595193
    Zbl07595193.

  7. Configuration Spaces of Manifolds with Boundary

    Authors
    Ricardo Campos, N. I., Pascal Lambrechts, Thomas Willwacher.
    Publication
    Astérisque 449 (2024), ISBN: 978-2-85629-990-6.
    Online on
    Online on .
    Accepted on
    Accepted on .
    Updated on
    Updated on .
    Full text
    Full text.
    10.24033/ast.1222
    10.24033/ast.1222.
    arXiv:1802.00716
    arXiv:1802.00716.
    hal-01721634
    hal-01721634.
    MR4764220
    MR4764220.
    Zbl07882597
    Zbl07882597.

  8. The Lambrechts–Stanley Model of Configuration Spaces

    Author
    N. I.
    Publication
    In: Invent. Math. (2019) 216.1, pp. 1–68.
    Online on
    Online on .
    Accepted on
    Accepted on .
    Updated on
    Updated on .
    Full text
    Full text.
    10.1007/s00222-018-0842-9
    10.1007/s00222-018-0842-9.
    arXiv:1608.08054
    arXiv:1608.08054.
    hal-01438861
    hal-01438861.
    MR3935037
    MR3935037.
    Zbl07051043
    Zbl07051043.

  9. Opérades et Structures Commutatives à Homotopie Près

    Author
    N. I.
    Publication
    In: Grad. J. Math. (2016) 1.1, pp. 9–17.
    Online on
    Online on .
    Full text
    Full text.
    hal-03997161
    hal-03997161.
    MR3848667
    MR3848667.
    Zbl1497.18028
    Zbl1497.18028.
    Journal
    Journal.

  10. Swiss-Cheese Operad and Drinfeld Center

    Author
    N. I.
    Publication
    In: Israel J. Math. (2017) 221.2, pp. 941–972.
    Online on
    Online on .
    Accepted on
    Accepted on .
    Updated on
    Updated on .
    Full text
    Full text.
    10.1007/s11856-017-1579-7
    10.1007/s11856-017-1579-7.
    arXiv:1507.06844
    arXiv:1507.06844.
    hal-01438863
    hal-01438863.
    MR3704940
    MR3704940.
    Zbl06808424
    Zbl06808424.

Theses

  1. Structure of Configuration Spaces

    Author
    N. I.
    Publication
    Habilitation à Diriger des Recherches (HDR), Université Paris Cité.
    Online on
    Online on .
    Full text
    Full text.
    Source
    Source.
    tel-05082275
    tel-05082275.
    Defense
    Defense.

  2. Operadic Formality and Homotopy of Configuration Spaces

    Author
    N. I.
    Publication
    Doctoral thesis, Université de Lille.
    Online on
    Online on .
    Full text
    Full text.
    Source
    Source.
    tel-01731389
    tel-01731389.
    University
    University.
    Defense
    Defense.

  3. Homologie et complexes de déformations d’opérades $E_n$

    Author
    N. I.
    Publication
    Master's thesis, Université Paris Diderot.
    Online on
    Online on .
    Full text
    Full text.