[français]

# Web page of Estanislao Herscovich

Institut Fourier-UMR 5582
100 rue des maths
38610 Gières
FRANCE

Office: 334
Tel. : 04 76 51 46 56

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.

You may find my CV here.

• Representation theory of associative algebras;

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

• Koszul algebras and generalisations, Yang-Mills algebras, down-up algebras;

• Quantum field theory, conformal field theory.

1. A simple note on the Yoneda (co)algebra of a monomial algebra. Accepted for publication in Ukraïn. Mat. Zh.

2. (jt. with D. Fernández) Cyclic $$A_{\infty}$$-algebras and double Poisson algebras. Accepted for publication in J. Noncommut. Geom.

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

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

5. On the Merkulov construction of $$A_{\infty}$$-(co)algebras. Ukraïn. Mat. Zh. 71 (2019), no. 8, 1133-1140. [Preprint].

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

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

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

9. 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].

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

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

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

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

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

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

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

17. (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.

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

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

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

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

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

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

24. (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.

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

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

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

28. (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].

• 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, I am a member of the ETC "Égalité femmes/hommes, diversité" [French] (optional cours "Equality women/men, diversity").