Our research group develops and improves methods of phylogenetic reconstruction based on mathematical tools, especially algebraic, semi-algebraic and geometrical tools. This involves studying molecular substitution models from a mathematical point of view to guarantee parameter identifiability and to provide model selection tools (including both the evolutionary model and the tree or network selection). Our research lies at the borders of phylogenetic reconstruction, algebraic statistics, algebraic geometry and computational algebra.



Marta Casanellas



After finishing my PhD in algebraic geometry at Universitat de Barcelona, I was awarded a Fulbright grant to do a postdoc at UC Berkeley under the supervision of Robin Hartshorne. Afterwards, I moved to Universitat Politècnica de Calaunya with a Ramon y Cajal contract. By that time, I started shifting interests towards the applications of algebraic geometry in phylogenetics. In this new field I have contributed by studying the geometry of evolutionary models and providing new methods of phylogenetic reconstruction that are based on algebraic techniques. I have produced more that fourty publications, alone or in collaboration with international researchers. I have been the principal investigator of a team of 20 scientists and I am nowadays a full professor at the Department of Mathematics at UPC.


Jesús Fernández



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.

Angélica Torres

Postdoctoral Researcher


Roser Homs

Postdoctoral Researcher


M. Casanellas, J. Fernández-Sánchez, J. Roca-Lacostena, The embedding problem for Markov matrices, Publicacions Matemàtiques (2023) 67(1), 411-445 READ
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 READ
M. Casanellas, S. Petrovic, C. Uhler, Algebraic Statistics in Practice: Applications to Networks, Annual Review of Statistics and its Applications (2020), vol. 7, 227-250 READ
M. Casanellas, J. Fernández-Sánchez, M. Michalek, Local equations for equivariant evolutionary models, Advances in Mathematics (2017) , 315, 285-323. READ
J. Fernández-Sánchez, M. Casanellas, Invariant versus classical approach when evolution is heterogeneous across sites and lineages, Systematic Biology (2016), 65 (2), 280-291. READ
M. Casanellas, J.Fernández-Sánchez, Relevant phylogenetic invariants of evolutionary models, J. Mathématiques Pures et Appliquées 96 (2011), 207-229. READ
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. READ
Michael D. Woodhams, Jesús Fernández-Sánchez, Jeremy G. Sumner, A New Hierarchy of Phylogenetic Models Consistent with Heterogeneous Substitution Rates, Systematic Biology 0(0):1-13 (2015) DOI: 10.1093/sysbio/syv021 READ
Software developed
Previous members (BSc or MSc project, PhD students or postdocs)