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Our group works on topological and differentiable manifolds, algebraic varieties, and their applications, viewing problems from a variety of different perspectives. The group has a long tradition working on various different interfaces of algebra, geometry and topology. In the last decade, we have become active contributors in interdisciplinary science and we are now focused on both a theoretical point of view and the transversal applications to several disciplines including Robotics, Machine Learning, Physics and Celestial Mechanics. Our research can be grouped in 8 different research lines which are closely related and interact in a dynamic manner. The 4  first lines are theoretical and the 4 last ones are interdisciplinary.

Most of the members are in more than one research line proving the multidisciplinary character of our research. Below we attach a diagram with the several research lines, their members and collaborators.


Research Lines


of the line

Other members


 Algebraic Geometry (AGE)


Barja, Alberich

Àlvarez, Amorós,  Fernández, Blanco, Pascual

Almirón, Dachs, González-Alonso, Michalska, Pardini, Stoppino

  Commutative Algebra and Number theory (CAN)

Àlvarez, Planas

Alberich, Blanco, Plans

Boix, Dachs, Huneke, Núñez-Betancourt, Zarzuela

New Challenges in Algebraic Topology (TOP)





Alberich, Amorós, Elgueta, Miranda,  Pascual, Roig

Cirici, Tonks, Kock, Ronco, Kaufmann, Vallette, Gepner, Gorbounov, Shaikh, Neumann, Alarcón-Heredia,

Whitehouse, Castellana, Casacuberta,

 New trends in Differential Geometry, Symplectic Geometry and Geometric Mechanics (SYM)


 Miranda, Muñoz

Braddell, Gràcia, Oms, Planas-Bahí, Román

Barbero, Bouloc,Delshams, Esposito, Guillemin, Martínez-Torres, Prieto, Rivas, Scott, Presas,Solha, Weitsman, Zung

Applications to Biology (BIO)




Roca, Garrote-López

  Alvarez-González, Cifuentes, Petrovick, Fisher, Kosta, Rodriguez-Rivas, Sumner

Applications to Control Theory, Machine Learning and Robotics (ROB)


Alberich, Muñoz

Amorós, Casanellas, Gràcia, Román

Alenyà, Thomas, Torras, Barbero, Cortés, Martínez, Ruffini, Gavaldà

Applications to Dynamical Systems and Celestial Mechanics (CEL)



Alberich, Braddell, Oms, Planas-Bahi

 Bouloc, Delshams, Ferragut, Llibre

Applications to Physics (PHY)


Amorós, Román


Gràcia, Miranda, Muñoz

Carrera, de Haro, Esposito, Gaset, Granados, Guillemin, Hamilton, Presas, Prieto, Rivas, Solha, Weitsman