Geometric methods are being of considerable interest in theoretical physics and engineering by the Finding of applications in the most advanced fields of research such as quantum mechanics, relativity and cosmology, field theories, thermodynamics, mechanics classical and fluid, numerical simulation of physical systems with applications to engineering, robotics, neuroscience, etc. From this perspective, ICMAT has a significant number of specialists in this field who have obtained relevant results in the area with important international connections. The objective of this thematic semester is to carry out activities focused on some of the most important research topics in this field trying to connect the research of the different groups, encouraging the training of new researchers with specific courses, and seeking to increase international collaboration.

Some topics that will be particularly affected are the following: Spectral theory, dynamics Hamiltonian and mechanical, dynamical, geometric and quantum control, discrete mechanics, information theory, variational methods, applications to biology, robotics, mechanical engineering and modern physics.