Higher Algebra, Geometry, and Topology

Book

• Maurer-Cartan methods in deformation theory: the twisting procedure, Vladimir Dotsenko, Sergey Shadrin, Bruno Vallette, London Mathematical Society Lecture Note Series, 488, Cambridge University Press, 2023, 186 pp.

Articles

• Persistent homology for functionals, Ulrich Bauer, Aníbal Medina-Mardones, and Maximilian Schmahl, to appear in Communications in Contemporary Mathematics.
• Associator dependent algebras and Koszul duality, Murray Bremner, Vladimir Dotsenko, Annali di Matematica Pura ed Applicata (1923- ), Volume 202, pages 1233–1254 (2023).
• Boardman–Vogt resolutions and bar/cobar constructions of (co)operadic (co)bimodules, Ricardo Campos, Julien Ducoulombier, Najib Idrissi High. Struct. 5(1):293–366 (2021).
• Operadic deformation theory, Ricardo Campos and Albin Grataloup, In: Vallette, B. (eds) Higher Structures and Operadic Calculus. Advanced Courses in Mathematics - CRM Barcelona. Birkhäuser, Cham, 2025, 59-158.
• An effective proof of the Cartan formula: Odd primes, Federico Cantero-Morán, Aníbal Medina-Mardones, Homology, Homotopy and Applications, 27 (2025), no. 1, 207–234.
• Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces, David Chataur, Joana Cirici, Transactions of the American Mathematical Society 375, no. 02, 925-960 (2022).
• Weight decompositions on algebraic models for mapping spaces and homotopy automorphisms, Joana Cirici, Bashar Saleh, Mediterranean Journal of Mathematics, 21 (2024), article 156.
• A_∞-structures for Bott-Chern and Aeppli cohomologies, Joana Cirici, Roger Garrido-Vilallave, Anna Sopena-Gilboy Complex Manifolds, 12 (2024), issue 1, article 20250012.
• An operadic proof of the BTT Theorem, Joana Cirici, Geoffroy Horel, to appear in Philosophical Transactions of the Royal Society A: Mathematical, Physical, and Engineering Sciences.
• Homotopy BV-algebras in Hermitian geometry, Joana Cirici, Scott O. Wilson, Journal of Geometry and Physics, 204 (2024), article 105275.
• Cup and Massey products on the cohomology of compact almost complex manifolds, Joana Cirici, Rivista di Matematica della Università di Parma, 13:2 (2022), 297–305..
• Étale cohomology, purity and formality with torsion coefficients, Joana Cirici, Geoffroy Horel, Journal of Topology 15:4 (2022), 2270-2297.
• Filtered A-infinity structures in complex geometry, Joana Cirici, Anna Sopena-Gilboy Proc. Amer. Math. Soc. 150, 4067-4082 (2022).
• Hodge-de Rham numbers of almost complex 4-manifolds, Joana Cirici, Scott O. Wilson, Expositiones Mathematicae, 40:4 (2022), 1244–1260.
• Matroids, Feynman categories, and Koszul duality, Basile Coron, Duke Mathematical Journal 174 (2025), no. 11, 2303–2381.
• Supersolvability of built lattices and Koszulness of generalized Chow rings, Basile Coron, to appear in Compositio Mathematica.
• Tridendriform algebras on hypergraph polytopes, Pierre-Louis Curien, Bérénice Delcroix-Oger, Jovana Obradović, Algebraic Combinatorics, Volume 8 (2025), no. 1, pp. 201-234.
• Some properties of the parking function poset, Bérénice Delcroix-Oger, Matthieu Josuat-Vergès, Lucas Randazzo, Electronic Journal of Combinatorics, Volume 29, Issue 4 (2022), article P4.42..
• Stable homology of Lie algebras of derivations and homotopy invariants of wheeled operads, Vladimir Dotsenko, Compositio Mathematica, Volume 161, Issue 4, pp. 756-799.
• Hidden structures behind ambient symmetries of the Maurer-Cartan equation, Vladimir Dotsenko, Sergey Shadrin, to appear in Homology, Homotopy and Applications.
• Polynomial identities in Novikov algebras, Vladimir Dotsenko, Nurlan Ismailov, Ualbai Umirbaev, Mathematische Zeitschrift, 303, 60 (2023).
• Reconnectads, Vladimir Dotsenko, Adam Keilthy, Denis Lyskov, Algebraic Combinatorics, 7 (2024) no. 3, pp. 801-842.
• Deformation theory of Cohomological Field Theories, Vladimir Dotsenko, Sergey Shadrin, Arkady Vaintrob, Bruno Vallette, Journal für die reine und angewandte Mathematik (Crelles Journal), 809 (2024), 91-157.
• A characterisation of Lie algebras using ideals and subalgebras, Vladimir Dotsenko, Xabier García-Martínez, Bulletin of London Mathematical Society, Volume 56, Issue7 (2024), 2408-2423.
• Fine structures inside the PreLie operad revisited, Vladimir Dotsenko, to appear in Journal of Combinatorial Algebra.
• On the conjecture of Shang about free alternative algebras, Vladimir Dotsenko, to appear in Israel Journal of Mathematics.
• Categorification of quiver diagonalization and Koszul algebras, Vladimir Dotsenko, Evgeny Feigin, Piotr Kucharski, Markus Reineke, to appear in Publications of the Research Institute for Mathematical Sciences.
• The three graces in the Tits--Kantor--Koecher category , Vladimir Dotsenko, Iryna Kashuba, Orbita Mathematicae, Vol. 2 (2025), No. 1, 83–101.
• Volume preservation of Butcher series methods from the operad viewpoint, Vladimir Dotsenko, Paul Laubie, International Mathematics Research Notices, Volume 2025, Issue 13, July 2025, article rnaf187.
• An effective criterion for Nielsen-Schreier varieties, Vladimir Dotsenko, Ualbai Umirbaev, International Mathematics Research Notices, Volume 2023, Issue 23, December 2023, Pages 20385–20432.
• Koszul algebras and Donaldson-Thomas invariants, Vladimir Dotsenko, Evgeny Feigin, Markus Reineke, Letters in Mathematical Physics, Volume 112, article number 106 (2022).
• Homotopical rigidity of the pre-Lie operad, Vladimir Dotsenko, Anton Khoroshkin, Proceedings of the American Mathematical Society, 152 (2024), no. 4, Pages 1355–1371.
• DT invariants from vertex algebras, Vladimir Dotsenko, Sergey Mozgovoy, Journal of the Institute of Mathematics of Jussieu, Volume 24 , Issue 1 (2025), 291-339.
• Generalized cohomological field theories in the higher order formalism, Vladimir Dotsenko, Sergey Shadrin, Pedro Tamaroff, Communications in Mathematical Physics, Volume 399, pages 1439–1500 (2023).
• Finite generation for Hochschild cohomology of Gorenstein monomial algebras, Vladimir Dotsenko, Vincent Gélinas, Pedro Tamaroff, Selecta Mathematica (N.S.), Volume 29, article number 14 (2023).
• Nilpotence, weak nilpotence, and the nil property in the nonassociative world: computations and conjectures, Vladimir Dotsenko, to appear in Experimental Mathematics.
• The localization spectral sequence in the motivic setting, Clément Dupont, Daniel Juteau, Algebraic and Geometric Topology 24 (2024), no. 3, 1431–1466.
• Weight structures and formality, Coline Emprin and Geoffroy Horel, In: Vallette, B. (eds) Higher Structures and Operadic Calculus. Advanced Courses in Mathematics - CRM Barcelona. Birkhäuser, Cham, 2025, 159-209.
• The Betti side of the double shuffle theory. I. The harmonic coproducts, Benjamin Enriquez, Hidekazu Furusho, Selecta Mathematica (N.S.) 27, paper 79 (2021).
• The Betti side of the double shuffle theory. II. Double shuffle relations for associators, Benjamin Enriquez, Hidekazu Furusho, Selecta Mathematica (N.S.) 29, paper 3 (2023).
• The Betti side of the double shuffle theory. III. Bitorsor structures, Benjamin Enriquez, Hidekazu Furusho, Selecta Mathematica (N.S.) 29, paper 27 (2023).
• The stabilizer bitorsors of the module and algebra harmonic coproducts are equal, Benjamin Enriquez, Hidekazu Furusho, Advances in Mathematics 463 (2025), Paper No. 110128, 29 pp.
• Flowing from intersection product to cup product, Greg Friedman, Aníbal Medina-Mardones, and Dev Sinha, to appear in Journal of Topology and Analysis.
• Large N phenomena and quantization of the Loday--Quillen--Tsygan theorem, Grégory Ginot, Owen Gwilliam, Alastair Hamilton, Mahmoud Zeinalian, Advances in Mathematics, 409 (2022), Paper No. 108631, 63 pp.
• Two remarks on spaces of maps between operads of little cubes, Geoffroy Horel, Manuel Krannich, Alexander Kupers, Higher Structures 9 (2025), no. 1, 329–339.
• Binomial rings and homotopy theory, Geoffroy Horel, Journal für die reine und angewandte Mathematik (Crelles Journal), 813 (2024), 283–305.
• Curved Koszul duality of algebras over unital versions of binary operads, Najib Idrissi, Journal of Pure and Applied Algebra, Volume 227, Issue 3, March 2023, Paper No. 107208 (2023).
• Non-formality of Voronov’s Swiss-Cheese operads, Najib Idrissi, Renato Vasconcellos Vieira, The Quarterly Journal of Mathematics, 75 (2024), no. 1, 63–95.
• Homotopy prefactorization algebras, Najib Idrissi, Eugene Rabinovich, Research in the Mathematical Sciences, Volume 11, article number 45, (2024). .
• On the wheeled PROP of stable cohomology of Aut(F_n) with bivariant coefficients, Nariya Kawazumi, Christine Vespa, Algebraic & Geometric Topology, 23:7 (2023) 3089–3128.
• The diagonal of the operahedra, Guillaume Laplante-Anfossi, Advance in Math. 405, paper 108494, 50 pp. (2022).
• The diagonal of the multiplihedra and the tensor product of A-infinity morphisms, Guillaume Laplante-Anfossi, Thibaut Mazuir, Journal de l’École polytechnique — Mathématiques, Tome 10 (2023), pp. 405-446..
• Hypertrees and embedding of the FMan operad, Paul Laubie, International Mathematics Research Notices, Volume 2025, Issue 15, August 2025, article rnaf233.
• An axiomatic characterization of Steenrod’s cup-i products, Aníbal Medina-Mardones, to appear in Journal of the European Mathematical Society.
• Adams' cobar construction as a monoidal E_∞-coalgebra model of the based loop space,, Aníbal Medina-Mardones, Manuel Rivera, Forum of Mathematics Sigma 12 (2024), Paper No. e62, 21 pp..
• Ranicki-Weiss assembly and the Steenrod constructions, Aníbal Medina-Mardones, Proceedings of the American Mathematical Society, 152 (2024), no. 5, 2249–2259.
• The diagonal of cellular spaces and effective algebro-homotopical constructions, Aníbal Medina-Mardones, EMS Surv. Math. Sci.10 (2023), no.2, 223–241.
• Multisimplicial chains and configuration spaces, Aníbal Medina-Mardones, Andrea Pizzi, Paolo Salvatore, Journal of Homotopy and Related Structures 19 (2024), no. 2, 275–296.
• A Pirashvili-type theorem for functors on non-empty finite sets, Geoffrey Powell, Christine Vespa Glasgow Mathematical Journal, Volume 65, Issue 1, 61 pp. (2023).
• Curved operadic calculus, Victor Roca i Lucio, Bulletin de la Société Mathématique de France, Volume 152 (2024), Issue 1, 45-147.
• The integration theory of curved absolute homotopy Lie algebras, Victor Roca i Lucio, Advances in Mathematics, Volume 448 (2024), article 109718.
• Absolute algebras, contramodules, and duality squares, Victor Roca i Lucio, Journal of Pure and Applied Algebra 229 (2025), no. 7, Paper No. 107998, 53 pp..
• On the functors associated with beaded open Jacobi diagrams, Christine Vespa, Publications of the Research Institute for Mathematical Sciences, 61 (2025), no. 3, 503–534.

Preprints

• PD Operads and Explicit Partition Lie Algebras, Lukas Brantner, Ricardo Campos, Joost Nuiten, arXiv:2104.03870.
• André—Quillen cohomology in the context of curved algebras, Joan Bellier-Millès, Sinan Yalin, arXiv:2401.14309.
• Equivariant formality of the little disks operad, Pedro Boavida, Joana Cirici, Geoffroy Horel, arXiv:2501.03726.
• Chain rule symmetry for singular SPDEs, Yvain Bruned, Vladimir Dotsenko, arXiv:2403.17066.
• Novikov algebras and multi-indices in regularity structures, Yvain Bruned, Vladimir Dotsenko, arXiv:2311.09091.
• Lie algebroids are curved Lie algebras, Damien Calaque, Ricardo Campos, Joost Nuiten, arXiv:2103.10728.
• Integration theory of Lie-graph algebras, Ricardo Campos, Bruno Vallette, arXiv:2510.06934.
• Universal constructions in homotopical algebra, Ricardo Campos, Bruno Vallette, 2510.06941.
• Model category structures on truncated multicomplexes for complex geometry, Joana Cirici, Muriel Livernet and Sarah Whitehouse, arXiv:2501.13509.
• Formality of hypercommutative algebras of Kähler and Calabi-Yau manifolds, Joana Cirici, Geoffroy Horel, arXiv:2302.08492.
• Lie-operads and operadic modules from poset cohomology, Bérénice Delcroix-Oger, Clément Dupont, arXiv:2505.06094.
• Cellular diagonals of permutahedra, Bérénice Delcroix-Oger, Guillaume Laplante-Anfossi, Vincent Pilaud, Kurt Stoeckl, arXiv:2308.12119.
• On the conjecture of Kashuba and Mathieu about free Jordan algebras, Vladimir Dotsenko, Irvin Roy Hentzel, arXiv:2507.00437.
• Regularized integrals and manifolds with log corners, Clément Dupont, Erik Panzer, Brent Pym, arXiv:2312.17720.
• Logarithmic morphisms, tangential basepoints, and little disks, Clément Dupont, Erik Panzer, Brent Pym, arXiv:2408.13108.
• Kaledin classes and formality criteria, Coline Emprin, arXiv:2404.17529.
• Properadic coformality of spheres , Coline Emprin and Alex Takeda, arXiv:2503.04297.
• Obstruction sequences to homotopy equivalences, Coline Emprin, arXiv:2509.17895.
• Natural transformations relating homotopy and singular homology functors, Benjamin Enriquez, Florence Lecomte, arXiv:2301.01157.
• On the homological interpretation of the prounipotent completion of the fundamental group, Benjamin Enriquez, Florence Lecomte, arXiv:2105.01338.
• Construction of Maurer-Cartan elements over configuration spaces of curves, Benjamin Enriquez, Federico Zerbini, arXiv:2110.09341.
• Analogues of hyperlogarithm functions on affine complex curves, Benjamin Enriquez, Federico Zerbini, arXiv:2212.03119.
• Elliptic hyperlogarithms, Benjamin Enriquez, Federico Zerbini, arXiv:2307.01833.
• Foundations of geometric cohomology: from co-orientations to product structures, Greg Friedman, Aníbal Medina-Mardones, Dev Sinha, arXiv:2212.07482.
• Simplicial properadic homotopy, Eric Hoffbeck, Johan Leray, Bruno Vallette, arXiv:2505.22004.
• Automorphisms of framed operads, Geoffroy Horel, Thomas Willwacher, arXiv:2403.11185.
• Combinatorics of pre-Lie products sharing a Lie bracket, Paul Laubie, arXiv:2309.05552.
• Pre-Calabi-Yau algebras and homotopy double Poisson gebras, Johan Leray, Bruno Vallette, arXiv:2203.05062.
• Higher Lie Theory, Daniel Robert-Nicoud, Bruno Vallette, arXiv:2010.10485.
• Cohomology of toric diagrams, Grigory Solomadin, arXiv:2401.14146.
• Effective integration of Lie type algebras, Bruno Vallette, arXiv:2510.10144.

PhD Theses

• Algebraic invariants of matroids and generalized operads, Basile Coron, PhD thesis of the University of Strasbourg defended on May 24, 2023, download here.
• Théorie de l'obstructions opéradiques à la formalité et aux équivalences d'homotopie, Coline Emprin, PhD thesis of the University Sorbonne Paris Nord defended on June 25, 2025, download here.
• Approximations cellulaires d’applications diagonales de polytopes opéradiques, Guillaume Laplante-Anfossi, PhD thesis of the University Sorbonne Paris Nord defended on June 27, 2022, download here.
• Combinatoire, homotopie et plongements d'opérades, Paul Laubie, PhD thesis of the University of Strasbourg defended on May 24, 2024, download here.
• The integration theory of curved absolute homotopy Lie algebras, Victor Roca i Lucio, PhD thesis of the University Sorbonne Paris Nord defended on July 4, 2022, download here.