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Web page of Estanislao Herscovich

Institut Fourier-UMR 5582
100 rue des maths
38610 Gières

Office: 334
Tel. : 04 76 33 57 84

Email: Estanislao.Herscovich [at] univ-grenoble-alpes.fr

I am Assistant Professor at the Institut Fourier, Université Grenoble Alpes, Grenoble (pronouns: he/him).

From January 2013 to December 2014, I was Assistant Professor at the Mathematics Departement, FCEyN, UBA (Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires), Buenos Aires, Argentina, and a research member of the CONICET, Argentina.

From March 2010 to November 2011 I was an Alexander von Humboldt post-doc at the Universität Bielefeld, Bielefeld, Germany.

Concerning my undergraduate studies, I did my Master thesis in Mathematics, entitled La homología de Hochschild-Mitchell de categorías lineales y su parecido con la homolgía de Hochschild de álgebras (Hochschild-Mitchell homology of linear categories and its resemblance with Hochschild homology of algebras), as well as my Master thesis in Physics, entitled Modelos de Wess-Zumino-Witten sobre \(\mathrm{SL}(2,\mathbb{R})\) y teoría de cuerdas (Wess-Zumino-Witten models on \(\mathrm{SL}(2,\mathbb{R})\) and string theory), at the Universidad de Buenos Aires.

I did my PhD thesis in Mathematics, Teoría de representaciones y homología de álgebras de Yang-Mills (Representation theory and homology of Yang-Mills algebras) at the Universidad de Buenos Aires. My advisor was Andrea Solotar.

I did my Habilitation à diriger des recherches, entitled Théorie des représentations et algèbre homologique (Representation theory and homological algebra), at the Institut Fourier, Université Grenoble Alpes, Grenoble.

  1. Vertex algebras and 2-monoidal categories. Accepted for publication in Math. Res. Lett.

  2. Cyclic \(A_{\infty}\)-algebras and cyclic homology. Accepted for publication in Homology Homotopy Appl.

  3. (jt. with D. Fernández) Double quasi-Poisson algebras are pre-Calabi-Yau. Accepted for publication in Internat. Math. Res. Notices.

  4. Yoneda \(A_{\infty}\)-algebras and lattices of vector spaces. J. Algebra. 608 (2022), 465-486. [Preprint].

  5. (jt. with D. Fernández) Cyclic \(A_{\infty}\)-algebras and double Poisson algebras. J. Noncommut. Geom. 15 (2021), no. 1, 241-278. [Preprint].

  6. A simple note on the Yoneda (co)algebra of a monomial algebra. Ukraïn. Mat. Zh. 73 (2021), no. 2, 275-277 (reprinted in Ukrainian Math. J. 73 (2021), no. 2, 320-322). [Preprint].

  7. Hochschild cohomology of filtered dg algebras. High. Struct. 4 (2020), no. 2, 167-182. [Preprint].

  8. An elementary computation of the cohomology of the Fomin-Kirillov algebra with 3 generators. Homology Homotopy Appl. 22 (2020), no. 2, 367-386. [Preprint].

  9. On the Merkulov construction of \(A_{\infty}\)-(co)algebras. Ukraïn. Mat. Zh. 71 (2019), no. 8, 1133-1140 (reprinted in Ukrainian Math. J. 71 (2020), no. 8, 1294-1302). [Preprint].

  10. The curved \(A_{\infty}\)-coalgebra of the Koszul codual of a filtered dg algebra. Glasg. Math. J. 61 (2019), no. 3, 575-600. [Preprint].

  11. (jt. with V. Dang) Renormalization of Quantum Field Theory on Riemannian manifolds. Rev. Math. Phys. 31 (2019), no. 06, 1950017, 30 pp. [Preprint].

  12. Hochschild (co)homology of Koszul dual pairs. J. Noncommut. Geom. 13 (2019), no. 1, 59-85. [Preprint].

  13. Applications of one-point extensions to compute the \(A_{\infty}\)-(co)module structure of several \(\operatorname{Ext}\) (resp., \(\operatorname{Tor}\)) groups. J. Pure Appl. Algebra 223 (2019), no. 3, 1054-1072. [Preprint].

  14. A higher homotopic extension of persistent (co)homology. J. Homotopy Relat. Struct. 13 (2018), no. 3, 599-633.

  15. On the definition of multi-Koszul modules. J. Algebra 499 (2018), 478-505.

  16. Using torsion theory to compute the algebraic structure of Hochschild (co)homology. Homology Homotopy Appl. 20 (2018), no. 1, 117-139.

  17. (jt. with S. Chouhy and A. Solotar) Hochschild homology and cohomology of down-up algebras. J. Algebra 498 (2018), 102-128.

  18. Spectral sequences associated to deformations. J. Homotopy Relat. Struct. 12 (2017), no. 3, 513-548.

  19. Noncommutative valuation of options. Rep. Math. Phys. 78 (2016), no. 3, 371-386.

  20. Some remarks on representations of Yang-Mills algebras. J. Math. Phys. 56 (2015), no. 1, 011702, 6 pp.

  21. (jt. with A. Solotar and M. Suárez-Álvarez) PBW-deformations and deformations à la Gerstenhaber of \(N\)-Koszul algebras. J. Noncommut. Geom. 8 (2014), no. 2, 505-539.

  22. On the multi-Koszul property for connected algebras. Doc. Math. 18 (2013), 1301-1347.

  23. Representations of super Yang-Mills algebras. Comm. Math. Phys. 320 (2013), no. 3, 783-820.

  24. (jt. with A. Rey) On a definition of multi-Koszul algebras. J. Algebra 376 (2013), 196-227. [Errata]

  25. The Dixmier map for nilpotent super Lie algebras. Comm. Math. Phys. 313 (2012), no. 2, 295-328.

  26. (jt. with A. Solotar) Hochschild and cyclic homology of Yang-Mills algebras. J. Reine Angew. Math. 665 (2012), 73-156.

  27. (jt. with A. Solotar) Representations of Yang-Mills algebras. Ann. of Math. (2) 173 (2011), no. 2, 1043-1080.

  28. (jt. with M. Richarte) Black holes in Einstein-Gauss-Bonnet gravity with a string cloud background. Phys. Lett. B 689 (2010), no. 4-5, 192-200.

  29. (jt. with A. Solotar) Derived invariance of Hochschild-Mitchell (co)homology and one-point extensions. J. Algebra 315 (2007), no. 2, 852-873.

  30. (jt. with A. Solotar) Hochschild-Mitchell cohomology and Galois extensions. J. Pure Appl. Algebra 209 (2007), no. 1, 37-55.

  31. (jt. with P. Minces and C. Núñez) Winding strings in \(\mathrm{AdS}_{3}\). J. High Energy Phys. 2006, no. 6, 047, 32 pp.

  32. (jt. with M. Ferreyra, A. Peuriot, G. Santiago and V. Slezak) Espectroscopía de absorción y optoacústica pulsada del \(\mathrm{NO}_{2}\)-\(\mathrm{N}_{2}\) en 532 nm. Anales AFA 16 (2005), no. 1, 63-65 [Spanish].

  1. Renormalization in Quantum Field Theory (after R. Borcherds). Astérisque No. 412 (2019), xvi+188. [Preprint].

  2. Teoría de representaciones y homología de álgebras de Yang-Mills: Un punto de vista algebraico sobre algunos aspectos de la teoría de gauge. Editorial Académica Española, (2012), 196 p. ISBN 978-3-8484-7496-7 [a published version of my PhD thesis, Spanish].

I am a strong supporter of equality and diversity, which is also supported by the Université Grenoble Alpes by means of the Charte pour une communication égalitaire et sans stéréotypes de sexe a l'Université Grenoble Alpes [French]. In particular, from 2019 to 2022 I was member of the ETC "Égalité femmes/hommes, diversité" [French] (optional cours "Equality women/men, diversity") and the program Égalité et lutte contre les discriminations [French] (Equality and fight against discrimination) of the UGA.