The unifying concept behind our project is the use of modern mathematical techniques to solve various problems in the frontiers of quantum field theory, enabling us to deal with questions like the quantization of space time, the issue of renormalization, algebraic and topological quantum field theories. Geometry and symmetry have always been a basic tool of scientific investigations. Their applications to modern physics, and quantum field theory in particular, have been immensely successful. The deformations of geometry and symmetries are at the basis of quantization and might be a key ingredient for further developments. The aim of our group is the use and developments of mathematical tools for the study of advanced quantum with a view to the applications mainly to quantum gravity and quantum spacetime, field theory, physics beyond the standard model, string theory and noncommutative geometry, but also more traditional particle phenomenology, condensed matter and application to biological systems.
The generalizations of geometry in which we work have had already an impact on the research in particle physics and gravitation. The approach to the standard model based on noncommutative geometry and the standard model, although still speculative, is getting closer to phenomenology, the Higgs and neutrinos. Topological and deformed field theories can be used for quantum gravity, and geometry is once again a useful tool for the understanding of the intricacies of renormalization.