Web page of Estanislao Herscovich

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.

• Representation theory of associative and Lie algebras;

• Homological algebra, Hoschschild and cyclic (co)homology;

• $A_{\infty}$-algebras, Koszul duality and generalisations;

• Quantum field theory, conformal field theory.

• (jt. with Z. Li) A projective resolution for the Fomin-Kirillov algebra $\operatorname{FK}(4)$.

• A remark on the monoidal structure of the category of $\mathbb{S}$-modules.

• Notes on dg (co)algebras and their (co)modules.

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

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

3. (jt. with Z. Li) Gerstenhaber structure on Hochschild cohomology of the Fomin-Kirillov algebra on 3 generators. Doc. Math. 27 (2022), 1773-1804. [Preprint].

4. Cyclic $A_{\infty}$-algebras and cyclic homology. Homology Homotopy Appl. 25 (2023), no. 1, 287-318. [Preprint].

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].

• Théorie des représentations et algèbre homologique (Representation theory and homological algebra). Defense of my Habilitation à diriger des recherches, at the Institut Fourier, Grenoble, France, December 1st, 2017 [French].

• $A_{\infty}$-algebras in representation theory and homological algebra. Plenary session at the XXI Coloquio Latinoamericano de Álgebra, Buenos Aires, Argentina, from July 25th to 29th, 2016.

• Ziling Li. PhD thesis: Cohomology of Fomin-Kirillov algebras. Institut Fourier, Université Grenoble Alpes, Grenoble, France, September 2023.

• Najib Mazid-Paula. Master 2 Recherche Mémoire: Catégories dérivées des modules différentiels gradués sur des algèbres différentielles graduées. Institut Fourier, Université Grenoble Alpes, Grenoble, France, June 2023 [French].

• Sofyan Al-haj Johnston. Projet de fin d'études du Magistère: Catégories dérivées des algèbres différentielles graduées. Université Grenoble Alpes, Grenoble, France, December 2022 [French].

• Jordan Beraud. Projet de fin d'études du Magistère: Étude d'$A_{\infty}$-algèbres. Université Grenoble Alpes, Grenoble, France, January 2022 [French].

• Gastón Barboza. Master thesis: Sobre la construcción geométrica del espectro de modelos de Wess-Zumino-Witten. Universidad de Buenos Aires, Argentina, September 2021 [Spanish].

• Marion Boucrot. Master 2 Recherche Mémoire: Algèbres de Frobenius et structure de double algèbre sur l'homologie de Hochschild. Institut Fourier, Université Grenoble Alpes, Grenoble, France, June 2021 [French].

• (co-supervided with G. McShane) Liticia Renault. UE Travail d'études et de recherche (TER): Loi de réciprocité quadratique. Université Grenoble Alpes, Grenoble, France, May 2021 [French].

• Matthis Martin. UE Travail d'études et de recherche (TER): Théorème "edge of the wedge". Université Grenoble Alpes, Grenoble, France, May 2021 [French].

• Habibatou Diallo. Projet de fin d'études du Magistère: Théorème de Serre-Swan sur les variétés lisses. Université Grenoble Alpes, Grenoble, France, January 2021 [French].

• Ziling Li. Master 2 Recherche Mémoire: Gröbner bases and Anick's resolution. Institut Fourier, Université Grenoble Alpes, Grenoble, France, June 2020.

• Habibatou Diallo. UE Travail d'études et de recherche (TER): Bases de Gröbner et algèbres de Fomin-Kirillov (duales). Université Grenoble Alpes, Grenoble, France, May 2020 [French].

• Valentine Soto. Projet de fin d'études du Magistère: Les algèbres vertex d'après Isaac Newton. Université Grenoble Alpes, Grenoble, France, January 2020 [French].

• Lucie Devey. UE Travail d'études et de recherche (TER): Le spin comme une conséquence de la théorie des représentations. Université Grenoble Alpes, Grenoble, France, May 2019 [French].

• Pierre Fromont. UE Travail d'études et de recherche (TER): Sur la conjecture jacobienne. Université Grenoble Alpes, Grenoble, France, May 2019 [French].

• Gabriel Palau. Master thesis: On the renormalization group of Quantum Field Theory (after R. Borcherds). Universidad de Buenos Aires, Argentina, March 2017.

• Enzo Sérandon. Master 2 Recherche Mémoire: $A_{\infty}$-structure sur la cogèbre $\operatorname{Tor}_{\bullet}^{A}(K,K)$ d'une algèbre monômiale. Institut Fourier, Université Grenoble Alpes, Grenoble, France, June 2016 [French].

• Virginia Gali. Master thesis: Quantum field theory and renormalization à la Stückelberg-Petermann-Epstein-Glaser. Universidad de Buenos Aires, Argentina, December 2015.

• Algèbre - MAT35b (Basic algebraic structures) for L3MA, Fall 2023 [French].

• MAT332 (Series et integration) for MINI, Fall 2023.

• Calcul différentiel L3B - MAT36f (Differential calculus) for L3B, Winter 2023 [French].

• Algèbre - MAT35b (Basic algebraic structures) for L3A, Fall 2022 [French].

• Soutien pour Algèbre - MAT35d (Extra tutoring on Basic algebraic structures) for L3B, Fall 2022 [French].

• MAT332 (Series et integration) for MINI, Fall 2022.

• MAT305 (Differential and matrix calculus) for CHI, Fall 2022 [French].

• Algèbre - MAT35b (Basic algebraic structures) for L3A, Fall 2021 [French].

• MAT332 (Series et integration) for MINI, Fall 2021.

• Géométrie différentielle et dynamique - MAT4213 (Basic differential geometry) for M1, Winter 2021 [French].

• Representation theory and homological algebra for the Master 2 degree in fundamental mathematics, Fall 2020.

• Introductory course: Fundamental groups, coverings and presentations of groups for the Master 2 degree in fundamental mathematics, Fall 2020.

• Algèbre 1 - MAT4111 (Basic commutative algebra and field extensions) for M1, Fall 2020 [French].

• MAT303 (Elementary topology and calculus of functions of several variables) for the group MAT, Fall 2020 [French].

• MAT366 (Riemann integration theory and probability) for the group L3B, Winter 2020 [French].

• Algèbre 1 - MAT4111 (Basic commutative algebra and field extensions) for M1, Fall 2019 [French].

• MAT303 (Elementary topology and calculus of functions of several variables) for the group MAT, Fall 2019 [French].

• MAT366 (Riemann integration theory and probability) for the group L3B, Winter 2019 [French].

• Algèbre 1 - MAT4111 (Basic commutative algebra and field extensions) for M1, Fall 2018 [French].

• MAT334 (Vector calculus and matrix calculus) for the group PCMI, Fall 2017.

• MAT334 (Vector calculus and matrix calculus) for the group PCMI, Fall 2016.

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.