(main)

research interests

I am part of Grupo de Teoría de Lie, a research group at FaMAF. My PhD advisor was Nicolás Andruskiewitsch.

I am interested in Hopf algebras and Nichols algebras. I study their classification and their representation theory.
In this framework, my favorite algebras are the Fomin-Kirrilov algebras \(FK_n\) and the generalized small quantum groups.
Two paradigmatic problems are surrounding my works and involve these algebras. First, it is not known whether or not
the Fomin-Kirillov algebras are finite or infinite dimensional for \(n \geq 6\). Second, most of my recent works are about
the representation theory of generalized small quantum groups. In the examples, I have observed that the Hilbert series
of their simple modules are palindromic and I would like to verify if this property holds true in general.

I received a Sandwich PhD Fellowship (2010) for studying at University of Antwerp under the supervision of Fred
Van Oystaeyen. I carried out a research stay (2017) in the Laboratoire de Mathématiques Blaise Pascal where
I was working together with Simon Riche and learning about Geometric Representation Theory, Derived
categories, Diagrammatic categories, Koszul duality, etc. Also, I performed a research stay (2019) in the
Instituto de Matemática de la Universidad de Sevilla collaborating with Luis Narváez.

See also my profiles in arXiv, Google Scholar, MathSciNet, ResearchGate and zbMATH.

collaborators

publications & preprints (and slides, posters and other stuff)

			Linkage principle for small quantum groups
			Koszul duality for Coxeter groups with S. Riche.
			The Green ring of a family of copointed Hopf algebras Rev. Un. Mat. Argentina, to appear.
			Simple modules of small quantum groups at dihedral groups Doc. Math. 29 (2024), no. 1, 1-38. with G. García.
			On the Hopf algebra structure of the Lusztig quantum divided power algebras Annales Mathématiques Blaise Pascal 27 (2020), no. 2, 131-157. with N. Andruskiewitsch and I. Angiono
			On Hopf algebras with triangular decomposition Contemp. Math. 728 (2019), 181-199.
			Mixed perverse sheaves on flag varieties of Coxeter groups Canad. J. Math. 72 (2020), no. 1, 1-55. with P. Achar and S. Riche.
			On the representation theory of the Drinfeld double of the Fomin-Kirillov algebra \(\mathcal{FK}_3\) Algebr. Represent. Theory 22 (2019), no. 6, 1399-1426. with B. Pogorelsky.
		GAP file	Copointed Hopf algebras over \(\mathbb{S}_4\) J. Pure Appl. Algebra 222 (2018), no. 9, 2784-2809. with A. García Iglesias.
			On projective modules over finite quantum groups Transf. Groups 24 (2019), no. 1, 279-299.
			Explicit coproduct formula for quantum group of the type \(G_2\) J. Algebra 500 (2018) 103-116. with V. Kharchenko.
			Verma and simple modules for quantum groups at non-abelian groups Adv. Math. 301 (2016) 423-457. with B. Pogorelsky.
			The cohomology ring of the 12-dimensional Fomin-Kirillov algebra Adv. Math. 291 (2016) 584-620. with D. Stefan.
			Acerca de las álgebras de Fomin-Kirillov Actas Congr. "Dr. Antonio A. R. Monteiro'' (2015), Univ. Nac. del Sur, Bahía Blanca, 43-54.
			Representations of copointed Hopf algebras arising from the tetrahedron rack Ann. Univ. Ferrara Sez. VII Sci. Mat. 60 (2014), no. 2, 407-427. with B. Pogorelsky.
			Finite-dimensional pointed or copointed Hopf algebras over affine racks J. Algebra 397 (2014) 379-406. with A. García Iglesias.
			Lifting via cocycle deformation J. Pure Appl. Algebra 218 (2014), no. 4, 684-703. with N. Andruskiewitsch , I. Angiono , A. García Iglesias and A. Masuoka.
			From Hopf algebras to tensor categories Conformal Field Theories and Tensor Categories, Yi-Zhu Huang et al. editors, Mathematical Lectures from Peking University, Springer. with N. Andruskiewitsch , I. Angiono , A. García Iglesias and B. Torrecillas.
			On a family of Hopf algebras of dimension 72 Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 3, 415-443. with N. Andruskiewitsch.
			Finite dimensional Hopf algebras over the dual group algebra of the symmetric group in three letters Comm. Algebra 39 (2011), no. 12, 4507-4517. with N. Andruskiewitsch.
			Hopf algebras of dimension 16 Algebr. Represent. Theory 13 (2010), no. 4, 383-405. with G. García.
			Aportes a la clasificación de las álgebras de Hopf (PhD Thesis) Director N. Andruskiewitsch. Fa.M.A.F., U.N.C. (2012).