Seminarium Gamma

This talk offers a concise overview of Lie systems, commemorating the 16th anniversary of my PhD defense. I will trace the historical development of Lie systems, beginning with foundational work by Guldberg, Vessiot, and Lie, which had a relevant moment in 1893 with the celebrated Lie theorem. This will be followed by the analysis of the contributions from Winternitz and the CRM school in Canada. My presentation will then explore the geometric approach (Carinena, Marmo, Grabowski) developed at the begining of my PhD. Then, I will explore the developments during my PhD thesis culminating with the coalgebra method (developed with my coworkers), deformation theory, Lie systems related to geometric structures, and other developments that followed after that. I will finish the newer approaches to Lie systems and their generalisations: stochastic and super Lie systems, discrete Lie systems, and Lie groupoid methods in Lie systems. I will also pay special attention to the results by Marmo, Carinena, Grundland, Ballesteros, Herranz, Fernandez-Sainz, Sardon, Campoamor-Stursberg, Carballal, Odzijewicz, Ibragimov, etc.