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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.

1.       AGE: Algebraic Geometry.
2.       CAN: Commutative Algebra and Number theory.
3.       TOP: New Challenges in Algebraic Topology.
4.       SYM: New trends in Differential Geometry, Symplectic Geometry and Geometric Mechanics.
5.       BIO: Applications to Biology
6.       ROB: Applications to Control Theory, Machine Learning and Robotics
7.       CEL: Applications to Dynamical Systems and Celestial Mechanics
8.       PHY:  Applications to Physics

    This research Project continues the geometric study of algebraic, symplectic and arithmetic varieties (DGICYT PS90-0069, PB93-0790, PB96-0234, BFM2000-0799, BFM2003-06001, BFM2003-02914, and DGI MTM2006-14234, MTM2012-38122-C03/FEDER) as well as the applications to Robotics, Computational Biology and Material Science started in the last project. The increasing interdisciplinarity of modern research and the fact that the boundaries between different areas of mathematics are vanishing, with a constant transfer of problems and techniques between them makes it difficult to progress without a multidisciplinary approach. In the present project we gather together experts in Algebraic, Symplectic and Arithmetic Geometry to stimulate the interaction between them and to allow the study of each object from different points of view.