I am an algebraist and my main research interest is the representation theory of finite dimensional Hopf algebras. I'm also interested in topological and geometrical aspects of related objects, as well as computational algebra and its applications, such as geometric aspects of data point clouds. In recent times I have been  working on factorization problems of operator algebras of smooth and analytic vectors over Lie Groups.

• M. Solís, A. Hernández: UMAP projections and the survival of empty space: A geometric approach to high dimensional data.  Data Science, Calssification and Artificial Intelligence for Modelig Decision Making, Springer (2025). doi.org/10.1007/978-3-031-85870-3 

• V. Gebhardt, A. Hernandez, F. Szechtman : Isomorphisms of relative holomorphs and matrix similarity. Bull. Aust. Math. Soc. (2024). doi: 10.1017/S0004972724000546 

• A. Hernández :  Minimum depth of factorization algebras. Revista Colombiana de Matemáticas. Vol 57, (2023)1, 87 - 101,https://doi.org/10.15446/recolma.v57n1.112374  Article 

• A. Hernández, M. Soís: Geometric goodness of fit measure to detect patterns in data point clouds. J. Comp. Stat. (2022), https://doi.org/10.1007/s00180-022-01244-1 . Article 

• J. Calvo, A. Hernández, M. Porter, F. Sanchez : A two-patch eoidemic model with nonlinear relapse. RMTA UCR, (2020), 27(01), 23-48. http://dx.doi.org/10.15517/rmta.v27i1.39946 . Article  

• A. Hernández, L. Kadison, S. Lopes : A quantum subgroup depth. A. Math. Hung. (2017), 152(01), 166-185. https://doi.org/10.1007/s10474-017-0694-6 . Article 

• A. Hernández, L. Kadison, M. Zamutolski : Subgroup depth and twisted coefficients. Comm. Alg. (2016), 44(8), 3570-3591. https://doi.org/10.1080/00927872.2015.1085994 . Article 

• A. Hernández, L. Kadison, C. Young : Algebraic quotient modules and subgroup depth. Abh. Sem. Math. Uni. Ham. (2014), 84, 267-283. https://doi.org/10.1007/s12188-014-0097-3  . Article 

• 2023 Spring - Summer, Mathematics department at the University of Ghent, Belgium : the representation theory of the small quantum group subalgebra extensions.

• 2025 - Winter, Mathmatics department at the University of Evora, Portugal. 

• 2025: A Coring type extesionf of Hopf algebras, University of Evora, Portugal.

• 2023: An overview on Depth theory. KU Leuven, Belgium. 

• 2023 : Hopf algebras as generalizations of group algebras. University of Ghent, Belgium. 

• 2022 : Geometric goodness of fit measure to detect patterns in data point clouds. COMPSTAT, Bologna, Italy :

• 2019 : Minimum depth and the Drinfel'd double. CLAM, Mexico City, Mexico.

• 2018 : Minimum depth and double cross products. XXV Escola Brasilerira de algebra, Campinas, Brazil.

• 2017 : Subalgebra depth and double cross products. Joint meeting RSME - SMA, Buenos Aires, Argentina.

• 2017 : A quantum subgroup depth. Integrable Systems and Quantum Dynamics, Prague, Czech Republic.

• 2015 : Subgroup depth, algebraic modules and twisted coefficients.  Joint meeting AMS - EMS, Porto Portugal. 

• 2015 :  Tensor powers of Galois corings. International colloquium in group theoretical methods in physics, Ghent, Belgium.