Shortly after finishing my doctoral thesis in singularity theory at the University of Barcelona, ​​I obtained a research grant (Juan de la Cierva program) to move to the Universitat Politècnica de Catalunya and continue working in geometry algebra and applications to phylogenetics. This research is mainly carried out in collaboration with Marta Casanellas, and focuses on the study of the geometry of evolutionary models  to devise new methods of phylogenetic reconstruction based on tools from algebraic geometry, commutative algebra, group representation theory and statistics. In 2010 I was invited by professors Peter Jarvis and Jeremy Sumner to stay at the University of Tasmania and collaborate in the design of models of nucleotide substitution with good mathematical properties. My research has given rise to more than 30 publications. Currently I'm an associate professor in the Department of Mathematics at the UPC.

Algebraic methods in Phylogenetics, Evolutionary models of Molecular substitution, Phylogenetic invariants, Singularity theory.

AGAUR Project 2017 SGR-93
MINECO/FEDER Projects MTM2015-69135, PID2019-103849GB-I00, MDM-2014-0445
CEX2020-001084-M (Spanish Government)

1. M. Casanellas, J. Fernández-Sánchez, J. Roca-Lacostena, The embedding problem for Markov matrices, Publicacions Matemàtiques (2023) 67(1), 411-445
2. M. Casanellas, J. Fernández-Sánchez, M. Garrote-López, SAQ: semi-algebraic quartet reconstruction method, IEEE/ Transactions on Computational Biology and Bioinformatics (2021), 18 (6), 2855-2861
3. M. Casanellas, J. Fernández-Sánchez, M. Michalek, Local equations for equivariant evolutionary models, Advances in Mathematics (2017) , 315, 285-323.
4. J. Fernández-Sánchez, M. Casanellas, Invariant versus classical approach when evolution is heterogeneous across sites and lineages, Systematic Biology (2016), 65 (2), 280-291.
5. M. Woodhams, J. Fernández-Sánchez, J. Sumner, A New Hierarchy of Phylogenetic Models Consistent with Heterogeneous Substitution Rates. Systematic Biology (2015)
6. M. Casanellas, J.Fernández-Sánchez, Relevant phylogenetic invariants of evolutionary models, J. Mathématiques Pures et Appliquées 96 (2011), 207-229.
7. M. Alberich-Carramiñana, J. Fernández-Sánchez, Equisingularity clases of birational projectiones of normal singularities to a plane, Advances in Mathematics 216 (2007) 753-770
8. M. Casanellas, J. Fernández-Sánchez, Performance of a new invariants method on homogeneous and non-homogeneous quartet trees, Molecular Biology and Evolution, 24(1):288-293, 2007.
9. J. Fernández-Sánchez, Equivalence of the Nash conjecture for primitive and sandwiched singularities. Proceedings of the America Mathematical Society 133 (2005) 677-679