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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. (jt. with Z. Li) Gerstenhaber structure on Hochschild cohomology of the Fomin-Kirillov algebra on 3 generators. Accepted for publication in Doc. Math.

  2. (jt. with Z. Li) Hochschild and cyclic (co)homology of the Fomin-Kirillov algebra on 3 generators. Accepted for publication in J. Noncommut. Geom.

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

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

  5. (jt. with D. Fernández) Double quasi-Poisson algebras are pre-Calabi-Yau. Int. Math. Res. Not. IMRN 2022, no. 23, 18291–18345. [Preprint].

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

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

  8. 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].

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

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

  11. 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].

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

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

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

  15. 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].

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

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

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

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

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

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

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

  23. (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.

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

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

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

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

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

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

  30. (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.

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

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

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

  34. (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.