Cartan and differential geometry, Lie theory, quantum groups and non commutative geometry For novel and Innovative Applications to quantum algorithms and geometric deep learning

Lie theory pervades all areas of mathematics, by providing natural encodings of symmetries; representation theory and Cartan geometry are two of its most successfull manifestations.CaLiForNIA aims to push the frontier of research in these two key topics, Lie Theory and Cartan Geometry in synergy with the complementary investigations in the areas of quantum groups and more generally non commutative geometry, including physical applications.

CaLiFornia goal is to apply the new mathematics originating by the above research to the new and strategic fields of quantum computing and geometric deep learning, top priorities in HorizonEurope.