Introduction

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	Coordinators of the line	Other members	Collaborators
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)	Gálvez	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	Gràcia, Oms, Planas-Bahí, Román	Barbero, Bouloc,Delshams, Esposito, Guillemin, Martínez-Torres, Prieto, Rivas, Scott, Presas,Solha, Weitsman, Zung
Applications to Biology (BIO)	Casanellas, Fernández-Sánchez	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)	Miranda	Alberich, 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