The project aims to develop knowledge in geometric mechanics, both from the theoretical point of view as well as that of applications to relevant physical and mathematical problems. Mainly the studies focus in topics of reduction by symmetry in field theory and discrete formalism to develop geometric integrators, that is, numerical methods that respect the geometric structures.
This project is centered around the following three research lines: (1) Geometric reduction in field theory, (2) Design and implementation of numerical integrators in optimal control problems and field theory, and (3) Applications of neural networks to mechanical problems with symmetry, constraints and controls.
The organization of this network is based in on-going collaborations that have already been materialized in publications and joint activities between the different groups being part of this network.
The members of this Thematic Network project center their work around these axis: Geometry, Mechanics and Control, all clearly interconnected.
The group has strong collaborative ties with researchers from:
Centro de Matemática de La Plata (Argentina). Researchers: María Emma Eyrea Irazú, María Eugenia García, Leandro Salomone, Cora Tori, Marcela Zuccalli.
Instituto Balseiro (Argentina). Researchers: Matías Caruso, Sergio Grillo.
Instituto de Ciencias Matemáticas (Spain): David Martín de Diego.
Universidad de La Laguna (Spain): Juan Carlos Marrero, Edith Padrón.
Universidad de Valencia (Spain): Cédric M. Campos.
University of Antwerp (Belgium): Tom Mestdag.
The members of the group have participated in several projects with researchers from other institutions such as:
“Reduction theory and numerical integration in mechanics and field theories”. Supporting entity: Universidad Nacional del Sur, Argentina. Main researcher: Santiago Capriotti. Years: 2018-2022.
"Mechanics systems, implicit differential equations, functional differential equations, integrability, and numerical methods in mechanics and control theory". Supporting entity: Agencia Nacional de Promoción Científica y Tecnológica, Argentina. Main researcher: Hernán Cendra. Years: 2014-2017.
"Geometric mechanics and theoretical physics". Supporting entity: Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina. Main researcher: Hugo Montani. Years: 2013-2016
"Mechanical systems, implicit differential equations, functional differential equations, and numerical methods in mechanics". Supporting entity: Agencia Nacional de Promoción Científica y Tecnológica, Argentina. Main researcher: Hernán Cendra. Years: 2011-2014.
"IRSES Network GEOMECH". Supporting entity: Marie Curie's International Research Staff Exchange Scheme, European Union. Main researcher: Frans Cantrijn. Years: 2011-2014.
"Geometric mechanics and quantum symmetries". Supporting entity: Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina. Main researcher: Roberto Trinchero. Years: 2011-2013.
"Implicit differential equations, mechanical systems and numerical integrators". Supporting entity: Agencia Nacional de Promoción Científica y Tecnológica, Argentina. Main researcher: Hernán Cendra. Years: 2007-2010.
"Differential geometry, mathematical physics and control theory". Supporting entity: Agencia Nacional de Promoción Científica y Tecnológica, Argentina. Main researcher: Jorge Solomín. Years: 2005-2008.